Edit Profile Tobiska, Lutz Compute Distance To: Compute Author ID: tobiska.lutz Published as: Tobiska, L.; Tobiska, Lutz Documents Indexed: 139 Publications since 1978, including 10 Books all top 5 Co-Authors 19 single-authored 28 Matthies, Gunar 13 Ganesan, Sashikumaar 11 Knobloch, Petr 11 Roos, Hans-Görg 10 Polevikov, Viktor Kuz’mich 10 Stynes, Martin 9 John, Volker 9 Schieweck, Friedhelm 6 Goering, Herbert 5 Lavrova, Olga 5 Lube, Gert 5 Skrzypacz, Piotr 4 Mitkova, Teodora 3 Ahmed, Naveed 3 Dorok, Ottfried 3 Franca, Leopoldo Luis Cabo Penna 3 Shaĭdurov, Vladimir Victorovich 3 Vassilevski, Panayot Spirov 2 Felgenhauer, Andreas 2 Hahn, Andreas 2 Layton, William J. 2 Linke, Alexander 2 Richter, Reinhard J. 2 Simon, Kristin 2 Thiele, Angela 2 Verfürth, Rüdiger 2 Xie, Hehu 1 Angermann, Lutz 1 Bänsch, Eberhard 1 Beresnev, Sergey 1 Burman, Erik 1 Eichel, Hagen 1 Franz, Sebastian 1 Gille, Marc 1 Gollwitzer, Christian 1 Gorbacheva, Yu. 1 Grambow, W. 1 He, Lianhua 1 Hysing, Shuren 1 Iliescu, Traian 1 Juhnke, Dominique 1 Kavaliou, Klim 1 Koeppe, G. 1 Kuzmin, Dmitri 1 Lange, Adrian 1 Lazarov, Raytcho D. 1 Lin, Qun 1 Madureira, Alexandre L. 1 Maubach, Joseph M. L. 1 Mitkova, T. I. 1 Parolini, Nicola 1 Petrova, Svetozara I. 1 Rehberg, Ingo 1 Risch, Uwe 1 Turek, Stefan 1 Valentin, Frédéric 1 Walkington, Noel J. 1 Winkel, Christian 1 Zarin, Helena 1 Zhou, Aihui all top 5 Serials 7 Computer Methods in Applied Mechanics and Engineering 6 IMA Journal of Numerical Analysis 6 Computing 5 SIAM Journal on Numerical Analysis 5 PAMM. Proceedings in Applied Mathematics and Mechanics 4 East-West Journal of Numerical Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 3 International Journal for Numerical Methods in Fluids 3 Mathematics of Computation 3 Numerische Mathematik 3 Applied Numerical Mathematics 3 Numerical Methods for Partial Differential Equations 3 Wissenschaftliche Zeitschrift der Technischen Universität Otto von Guericke Magdeburg 3 Mathematical Modelling and Analysis 3 Wissenschaftliche Zeitschrift der Technischen Hochschule Otto von Guericke 2 Journal of Computational Physics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Applied Mathematics and Computation 2 Zeitschrift für Analysis und ihre Anwendungen 2 Journal of Computational Mathematics 2 Numerical Algorithms 2 Computational Methods in Applied Mathematics 2 International Journal of Numerical Analysis and Modeling 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Springer Series in Computational Mathematics 2 Beiträge zur Analysis 1 Computers & Mathematics with Applications 1 Fluid Dynamics 1 Journal of Fluid Mechanics 1 Commentationes Mathematicae Universitatis Carolinae 1 Journal of Computational and Applied Mathematics 1 Mathematische Nachrichten 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 CWI Quarterly 1 Journal of Scientific Computing 1 Wissenschaftliche Zeitschrift der Technischen Hochschule Carl Schorlemmer Leuna-Merseburg 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Siberian Journal of Computer Mathematics 1 Computing and Visualization in Science 1 International Journal of Computational Fluid Dynamics 1 Abstract and Applied Analysis 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Multiscale Modeling & Simulation 1 Oberwolfach Reports 1 GAMM-Mitteilungen 1 Seminarbericht, Humboldt-Universität zu Berlin, Sektion Mathematik 1 International Journal of Computing Science and Mathematics 1 Cambridge-IISc Series all top 5 Fields 82 Numerical analysis (65-XX) 75 Fluid mechanics (76-XX) 53 Partial differential equations (35-XX) 8 Ordinary differential equations (34-XX) 5 General and overarching topics; collections (00-XX) 3 Mechanics of deformable solids (74-XX) 3 Biology and other natural sciences (92-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 97 Publications have been cited 2,058 times in 1,469 Documents Cited by ▼ Year ▼ Numerical methods for singularly perturbed differential equations. Convection-diffusion and flow problems. Zbl 0844.65075Roos, Hans-Görg; Stynes, Martin; Tobiska, Lutz 442 1996 Robust numerical methods for singularly perturbed differential equations. Convection-diffusion-reaction and flow problems. 2nd ed. Zbl 1155.65087Roos, Hans-Görg; Stynes, Martin; Tobiska, Lutz 333 2008 A two-level method with backtracking for the Navier-Stokes equations. Zbl 0913.76050Layton, W.; Tobiska, L. 102 1998 Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122Lin, Qun; Tobiska, Lutz; Zhou, Aihui 99 2005 A unified convergence analysis for local projection stabilisations applied to the Oseen problem. Zbl 1188.76226Matthies, Gunar; Skrzypacz, Piotr; Tobiska, Lutz 85 2007 Quantitative benchmark computations of two-dimensional bubble dynamics. Zbl 1273.76276Hysing, S.; Turek, S.; Kuzmin, D.; Parolini, N.; Burman, E.; Ganesan, S.; Tobiska, L. 84 2009 Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations. Zbl 0843.76052Tobiska, Lutz; Verfürth, Rüdiger 54 1996 The SDFEM for a convection-diffusion problem with a boundary layer: Optimal error analysis and enhancement of accuracy. Zbl 1055.65121Stynes, Martin; Tobiska, Lutz 48 2003 On spurious velocities in incompressible flow problems with interfaces. Zbl 1173.76338Ganesan, Sashikumaar; Matthies, Gunar; Tobiska, Lutz 41 2007 Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems. Zbl 0898.65068John, V.; Maubach, J. M.; Tobiska, L. 30 1997 A finite difference analysis of a streamline diffusion method on a Shishkin mesh. Zbl 0916.65108Stynes, Martin; Tobiska, Lutz 29 1998 Using rectangularqpelements in the SDFEM for a convection-diffusion problem with a boundary layer. Zbl 1154.65083Stynes, Martin; Tobiska, Lutz 28 2008 Robust arbitrary order mixed finite element methods for the incompressible Stokes equations with pressure independent velocity errors. Zbl 1381.76186Linke, Alexander; Matthies, Gunar; Tobiska, Lutz 22 2016 Local projection stabilization of equal order interpolation applied to the Stokes problem. Zbl 1198.65214Ganesan, Sashikumaar; Matthies, Gunar; Tobiska, Lutz 22 2008 Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. Zbl 1171.65074Matthies, Gunar; Skrzypacz, Piotr; Tobiska, Lutz 22 2008 The inf-sup condition for the mapped \(Q_k-P_{k-1}^{\text{disc}}\) element in arbitrary space dimensions. Zbl 1016.65073Matthies, G.; Tobiska, L. 22 2002 A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems. Zbl 0942.76041John, V.; Matthies, G.; Schieweck, F.; Tobiska, L. 21 1998 Analysis of a new stabilized higher order finite element method for advection-diffusion equations. Zbl 1120.76336Tobiska, Lutz 20 2006 Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants. Zbl 1402.76072Ganesan, Sashikumaar; Tobiska, Lutz 19 2012 Stabilization by local projection for convection-diffusion and incompressible flow problems. Zbl 1203.76138Ganesan, Sashikumaar; Tobiska, Lutz 18 2010 A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants. Zbl 1282.76118Ganesan, Sashikumaar; Tobiska, Lutz 17 2009 Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier-Stokes equations. Zbl 0979.76047John, Volker; Tobiska, Lutz 17 2000 A modified streamline diffusion method for solving the stationary Navier- Stokes equation. Zbl 0696.76034Tobiska, Lutz; Lube, Gert 17 1991 Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems. Zbl 1228.76078Ahmed, N.; Matthies, G.; Tobiska, L.; Xie, H. 16 2011 A numerical study of a class of LES models. Zbl 1148.76327Iliescu, T.; John, V.; Layton, W. J.; Matthies, G.; Tobiska, L. 16 2003 A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes equation. Zbl 0681.76032Schieweck, F.; Tobiska, L. 16 1989 Singularly perturbed differential equations. Zbl 0522.35003Goering, Herbert; Felgenhauer, Andreas; Lube, Gert; Roos, Hans-Goerg; Tobiska, Lutz 16 1983 An accurate finite element scheme with moving meshes for computing 3D-axisymmetric interface flows. Zbl 1138.76045Ganesan, Sashikumaar; Tobiska, Lutz 15 2008 Convergence analysis of a multiscale finite element method for singularly perturbed problems. Zbl 1091.65108Franca, Leopoldo P.; Madureira, Alexandre L.; Tobiska, Lutz; Valentin, Frédéric 15 2005 Non-nested multi-level solvers for finite element discretisations of mixed problems. Zbl 1006.65137John, V.; Knobloch, P.; Matthies, G.; Tobiska, L. 15 2002 The streamline-diffusion method for nonconforming \(Q_1^{\text{rot}}\) elements on rectangular tensor-product meshes. Zbl 0980.65125Stynes, Martin; Tobiska, Lutz 15 2001 Aspects of finite element discretizations for solving the Boussinesq approximation of the Navier-Stokes equations. Zbl 0876.76038Dorok, O.; Grambow, W.; Tobiska, L. 15 1994 Local projection type stabilization applied to inf-sup stable discretizations of the Oseen problem. Zbl 1310.76095Matthies, Gunar; Tobiska, Lutz 14 2015 On the stability of finite-element discretizations of convection-diffusion-reaction equations. Zbl 1211.65147Knobloch, Petr; Tobiska, Lutz 14 2011 The \(P_1^{\text{mod}}\)-element: A new nonconforming finite element for convection-diffusion problems. Zbl 1048.65111Knobloch, Petr; Tobiska, Lutz 14 2003 The two-level local projection stabilization as an enriched one-level approach. Zbl 1253.65171He, Lianhua; Tobiska, Lutz 12 2012 The convergence of the cascadic conjugate-gradient method applied to elliptic problems in domains with re-entrant corners. Zbl 0947.65037Shaidurov, Vladimir; Tobiska, Lutz 12 2000 Necessary \(L^ 2\)-uniform convergence conditions for difference schemes for two-dimensional convection-diffusion problems. Zbl 0822.65077Stynes, M.; Tobiska, L. 12 1995 Robust a posteriori error estimates for stabilized finite element methods. Zbl 1334.65186Tobiska, L.; Verfürth, R. 11 2015 Stability of the residual free bubble method for bilinear finite elements on rectangular grids. Zbl 1005.65122Franca, Leopoldo P.; Tobiska, Lutz 11 2002 An optimal order error estimate for an upwind discretization of the Navier-Stokes equations. Zbl 0856.76037Schieweck, F.; Tobiska, L. 11 1996 Modelling and simulation of moving contact line problems with wetting effects. Zbl 1410.76173Ganesan, Sashikumaar; Tobiska, Lutz 10 2009 The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation. Zbl 1106.76305Gollwitzer, Christian; Matthies, Gunar; Richter, Reinhard; Rehberg, Ingo; Tobiska, Lutz 10 2007 Inf-sup stable nonconforming finite elements of arbitrary order on triangles. Zbl 1089.65123Matthies, Gunar; Tobiska, Lutz 10 2005 A nonconforming finite element method of streamline diffusion type for the incompressible Navier-Stokes equations. Zbl 0699.76032Lube, G.; Tobiska, L. 10 1990 The two-level local projection stablization as an enriched one-level approach, a one-dimensional study. Zbl 1198.65128Tobiska, Lutz; Winkel, Christian 9 2010 Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers. Zbl 0986.65109Stynes, M.; Tobiska, L. 8 2001 The streamline-diffusion method for conforming and nonconforming finite elements of lowest order applied to convection-diffusion problems. Zbl 0998.65118Matthies, G.; Tobiska, L. 8 2001 Streamline diffusion least-squares mixed finite element methods for convection-diffusion problems. Zbl 0895.65049Lazarov, R. D.; Tobiska, L.; Vassilevski, P. S. 8 1997 Supercloseness and superconvergence of stabilized low-order finite element discretizations of the Stokes problem. Zbl 1410.76168Eichel, Hagen; Tobiska, Lutz; Xie, Hehu 7 2011 Mass conservation of finite element methods for coupled flow-transport problems. Zbl 1185.65214Matthies, G.; Tobiska, L. 7 2007 Full and weighted upwind finite element methods. Zbl 0685.65074Tobiska, Lutz 7 1989 Finite elements. Theory and algorithms. Zbl 1382.65396Ganesan, Sashikumaar; Tobiska, Lutz 6 2017 On the relationship of local projection stabilization to other stabilized methods for one-dimensional advection-diffusion equations. Zbl 1229.76059Tobiska, Lutz 6 2009 Recent results on local projection stabilization for convection-diffusion and flow problems. Zbl 1180.35032Tobiska, Lutz 6 2009 Non-nested multi-grid solvers for mixed divergence-free scott-vogelius discretizations. Zbl 1175.65144Linke, Alexander; Matthies, Gunar; Tobiska, Lutz 6 2008 An inf-sup stable and residual-free bubble element for the Oseen equations. Zbl 1153.76040Franca, Leopoldo P.; John, Volker; Matthies, Gunar; Tobiska, Lutz 6 2007 Superconvergence of a 3D finite element method for stationary Stokes and Navier-Stokes problems. Zbl 1078.65091Matthies, G.; Skrzypacz, P.; Tobiska, L. 6 2005 Finite element methods for coupled problems in ferrohydrodynamics. Zbl 1138.76385Lavrova, Olga; Matthies, Gunar; Mitkova, Teodora; Polevikov, Viktor; Tobiska, Lutz 6 2003 Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem. Zbl 1343.76019Knobloch, Petr; Tobiska, Lutz 5 2013 On the solution of the steady-state diffusion problem for ferromagnetic particles in a magnetic fluid. Zbl 1255.76127Polevikov, V.; Tobiska, L. 5 2008 Finite element methods of an operator splitting applied to population balance equations. Zbl 1242.65199Ahmed, Naveed; Matthies, Gunar; Tobiska, Lutz 4 2011 Numerical study of soliton-like surface configurations on a magnetic fluid layer in the Rosensweig instability. Zbl 1221.76227Lavrova, Olga; Matthies, Gunar; Tobiska, Lutz 4 2008 Numerical modeling of the equilibrium shapes of a ferrofluid drop in an external magnetic field. Zbl 1354.76138Lavrova, O.; Matthies, G.; Polevikov, V.; Tobiska, L. 4 2004 A coupled multigrid method for nonconforming finite element discretizations of the 2D-Stokes equation. Zbl 0963.65126John, V.; Tobiska, L. 4 2000 Stabilization methods of bubble type for the \(Q_1/Q_1\)-element applied to the incompressible Navier-Stokes equations. Zbl 0984.76047Knobloch, Petr; Tobiska, Lutz 4 2000 Parallel finite element methods for the incompressible Navier-Stokes equations. Zbl 0876.76039Dorok, O.; John, V.; Risch, U.; Schieweck, F.; Tobiska, L. 4 1996 A new approach to recovery of discontinuous Galerkin. Zbl 1212.65444Franz, Sebastian; Tobiska, Lutz; Zarin, Helena 3 2009 On Korn’s first inequality for quadrilateral nonconforming finite elements of first-order approximation properties. Zbl 1106.65096Knobloch, Petr; Tobiska, Lutz 3 2005 Stabilized finite element methods for the Navier-Stokes problem. Zbl 0793.76053Tobiska, Lutz 3 1993 Diskretisierungsverfahren zur Lösung singulär gestörter Randwertprobleme. Zbl 0535.65058Tobiska, L. 3 1983 A finite element method for a noncoercive elliptic problem with Neumann boundary conditions. Zbl 1284.65169Kavaliou, Klim; Tobiska, Lutz 2 2012 A two-level local projection stabilisation on uniformly refined triangular meshes. Zbl 1255.65223Matthies, Gunar; Tobiska, Lutz 2 2012 ADI approach to the particle diffusion problem in magnetic fluids. Zbl 1386.76116Polevikov, V.; Tobiska, L. 2 2011 Linear and nonlinear approach to the Rosensweig instability. Zbl 1122.76037Lange, Adrian; Richter, Reinhard; Tobiska, Lutz 2 2007 Finite element simulation of a droplet impinging a horizontal surface. Zbl 1402.76071Ganesan, Sashikumaar; Tobiska, Lutz 2 2005 A streamline diffusion method for nonconforming finite element approximations applied to the linearized incompressible Navier-Stokes equation. Zbl 1119.76352Knobloch, P.; Tobiska, L. 2 1999 Error estimates and numerical experiments for streamline-diffusion-type methods on arbitrary and Shishkin meshes. Zbl 0908.65069Stynes, Martin; Tobiska, Lutz 2 1997 Finite element method. An introduction. 3., überarb. u. erw. Aufl. Zbl 0780.65066Goering, Herbert; Roos, Hans-Görg; Tobiska, Lutz 2 1993 Construction of \(L^2\)-orthogonal elements of arbitrary order for local projection stabilization. Zbl 1427.65258Schieweck, F.; Skrzypacz, P.; Tobiska, L. 1 2018 ALE-FEM for two-phase and free surface flows with surfactants. Zbl 1444.76043Ganesan, Sashikumaar; Hahn, Andreas; Simon, Kristin; Tobiska, Lutz 1 2017 Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems. Zbl 1273.65144Ganesan, Sashikumaar; Tobiska, Lutz 1 2013 A local projection type stabilization with exponential enrichments applied to one-dimensional advection-diffusion equations. Zbl 1239.65049Juhnke, Dominique; Tobiska, Lutz 1 2012 Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles. Zbl 1426.76169Lavrova, O.; Polevikov, V.; Tobiska, L. 1 2010 A finite element method for the simulation of a liquid droplet impinging on a solid surface. Zbl 1156.76032Ganesan, S.; Tobiska, L. 1 2008 Numerical simulation of the flow in magnetic fluid rotary shaft seals. Zbl 1151.76557Mitkova, Teodora; Tobiska, Lutz 1 2004 Modeling of a dynamic magneto-fluid seal in the presence of a pressure drop. Zbl 1175.76113Polevikov, V. K.; Tobiska, L. 1 2001 Simulation of free surfaces of magnetic liquids. Zbl 1057.76549Matthies, Gunar; Tobiska, Lutz 1 2001 Modified FE discretizations of incompressible flow problems and their relationship to stabilized methods. Zbl 1006.76057Knobloch, Petr; Tobiska, Lutz 1 2000 A comparison of three solvers for the incompressible Navier-Stokes equations. Zbl 0985.76053John, V.; Matthies, G.; Mitkova, T. I.; Tobiska, L.; Vassilevski, P. S. 1 2000 Analysis of a mathematical model related to Czochralski crystal growth. Zbl 0969.35107Knobloch, Petr; Tobiska, Lutz 1 1998 Special integration formulae for a convection-diffusion problem. Zbl 0839.65117Shaidurov, V.; Tobiska, L. 1 1995 Finite element methods of streamline diffusion type for the Navier-Stokes equations. Zbl 0744.76080Tobiska, L. 1 1991 Eine upwind FEM zur Lösung des stationären Navier-Stokes Problems. (An upwind FEM for the solution of the stationary Navier-Stokes problem). Zbl 0638.76032Schieweck, Friedhelm; Tobiska, Lutz 1 1987 An enclosure generating modification of the method of discretization in time. Zbl 0635.65122Koeppe, G.; Roos, H.-G.; Tobiska, L. 1 1987 Die asymptotische Lösung singulär gestörter elliptischer Probleme 2. Ordnung. Zbl 0479.35009Tobiska, Lutz; Lube, Gert 1 1980 Asymptotische Lösung singulär gestörter Probleme. Zbl 0421.35005Tobiska, Lutz 1 1978 Construction of \(L^2\)-orthogonal elements of arbitrary order for local projection stabilization. Zbl 1427.65258Schieweck, F.; Skrzypacz, P.; Tobiska, L. 1 2018 Finite elements. Theory and algorithms. Zbl 1382.65396Ganesan, Sashikumaar; Tobiska, Lutz 6 2017 ALE-FEM for two-phase and free surface flows with surfactants. Zbl 1444.76043Ganesan, Sashikumaar; Hahn, Andreas; Simon, Kristin; Tobiska, Lutz 1 2017 Robust arbitrary order mixed finite element methods for the incompressible Stokes equations with pressure independent velocity errors. Zbl 1381.76186Linke, Alexander; Matthies, Gunar; Tobiska, Lutz 22 2016 Local projection type stabilization applied to inf-sup stable discretizations of the Oseen problem. Zbl 1310.76095Matthies, Gunar; Tobiska, Lutz 14 2015 Robust a posteriori error estimates for stabilized finite element methods. Zbl 1334.65186Tobiska, L.; Verfürth, R. 11 2015 Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem. Zbl 1343.76019Knobloch, Petr; Tobiska, Lutz 5 2013 Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems. Zbl 1273.65144Ganesan, Sashikumaar; Tobiska, Lutz 1 2013 Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants. Zbl 1402.76072Ganesan, Sashikumaar; Tobiska, Lutz 19 2012 The two-level local projection stabilization as an enriched one-level approach. Zbl 1253.65171He, Lianhua; Tobiska, Lutz 12 2012 A finite element method for a noncoercive elliptic problem with Neumann boundary conditions. Zbl 1284.65169Kavaliou, Klim; Tobiska, Lutz 2 2012 A two-level local projection stabilisation on uniformly refined triangular meshes. Zbl 1255.65223Matthies, Gunar; Tobiska, Lutz 2 2012 A local projection type stabilization with exponential enrichments applied to one-dimensional advection-diffusion equations. Zbl 1239.65049Juhnke, Dominique; Tobiska, Lutz 1 2012 Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems. Zbl 1228.76078Ahmed, N.; Matthies, G.; Tobiska, L.; Xie, H. 16 2011 On the stability of finite-element discretizations of convection-diffusion-reaction equations. Zbl 1211.65147Knobloch, Petr; Tobiska, Lutz 14 2011 Supercloseness and superconvergence of stabilized low-order finite element discretizations of the Stokes problem. Zbl 1410.76168Eichel, Hagen; Tobiska, Lutz; Xie, Hehu 7 2011 Finite element methods of an operator splitting applied to population balance equations. Zbl 1242.65199Ahmed, Naveed; Matthies, Gunar; Tobiska, Lutz 4 2011 ADI approach to the particle diffusion problem in magnetic fluids. Zbl 1386.76116Polevikov, V.; Tobiska, L. 2 2011 Stabilization by local projection for convection-diffusion and incompressible flow problems. Zbl 1203.76138Ganesan, Sashikumaar; Tobiska, Lutz 18 2010 The two-level local projection stablization as an enriched one-level approach, a one-dimensional study. Zbl 1198.65128Tobiska, Lutz; Winkel, Christian 9 2010 Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles. Zbl 1426.76169Lavrova, O.; Polevikov, V.; Tobiska, L. 1 2010 Quantitative benchmark computations of two-dimensional bubble dynamics. Zbl 1273.76276Hysing, S.; Turek, S.; Kuzmin, D.; Parolini, N.; Burman, E.; Ganesan, S.; Tobiska, L. 84 2009 A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants. Zbl 1282.76118Ganesan, Sashikumaar; Tobiska, Lutz 17 2009 Modelling and simulation of moving contact line problems with wetting effects. Zbl 1410.76173Ganesan, Sashikumaar; Tobiska, Lutz 10 2009 On the relationship of local projection stabilization to other stabilized methods for one-dimensional advection-diffusion equations. Zbl 1229.76059Tobiska, Lutz 6 2009 Recent results on local projection stabilization for convection-diffusion and flow problems. Zbl 1180.35032Tobiska, Lutz 6 2009 A new approach to recovery of discontinuous Galerkin. Zbl 1212.65444Franz, Sebastian; Tobiska, Lutz; Zarin, Helena 3 2009 Robust numerical methods for singularly perturbed differential equations. Convection-diffusion-reaction and flow problems. 2nd ed. Zbl 1155.65087Roos, Hans-Görg; Stynes, Martin; Tobiska, Lutz 333 2008 Using rectangularqpelements in the SDFEM for a convection-diffusion problem with a boundary layer. Zbl 1154.65083Stynes, Martin; Tobiska, Lutz 28 2008 Local projection stabilization of equal order interpolation applied to the Stokes problem. Zbl 1198.65214Ganesan, Sashikumaar; Matthies, Gunar; Tobiska, Lutz 22 2008 Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. Zbl 1171.65074Matthies, Gunar; Skrzypacz, Piotr; Tobiska, Lutz 22 2008 An accurate finite element scheme with moving meshes for computing 3D-axisymmetric interface flows. Zbl 1138.76045Ganesan, Sashikumaar; Tobiska, Lutz 15 2008 Non-nested multi-grid solvers for mixed divergence-free scott-vogelius discretizations. Zbl 1175.65144Linke, Alexander; Matthies, Gunar; Tobiska, Lutz 6 2008 On the solution of the steady-state diffusion problem for ferromagnetic particles in a magnetic fluid. Zbl 1255.76127Polevikov, V.; Tobiska, L. 5 2008 Numerical study of soliton-like surface configurations on a magnetic fluid layer in the Rosensweig instability. Zbl 1221.76227Lavrova, Olga; Matthies, Gunar; Tobiska, Lutz 4 2008 A finite element method for the simulation of a liquid droplet impinging on a solid surface. Zbl 1156.76032Ganesan, S.; Tobiska, L. 1 2008 A unified convergence analysis for local projection stabilisations applied to the Oseen problem. Zbl 1188.76226Matthies, Gunar; Skrzypacz, Piotr; Tobiska, Lutz 85 2007 On spurious velocities in incompressible flow problems with interfaces. Zbl 1173.76338Ganesan, Sashikumaar; Matthies, Gunar; Tobiska, Lutz 41 2007 The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation. Zbl 1106.76305Gollwitzer, Christian; Matthies, Gunar; Richter, Reinhard; Rehberg, Ingo; Tobiska, Lutz 10 2007 Mass conservation of finite element methods for coupled flow-transport problems. Zbl 1185.65214Matthies, G.; Tobiska, L. 7 2007 An inf-sup stable and residual-free bubble element for the Oseen equations. Zbl 1153.76040Franca, Leopoldo P.; John, Volker; Matthies, Gunar; Tobiska, Lutz 6 2007 Linear and nonlinear approach to the Rosensweig instability. Zbl 1122.76037Lange, Adrian; Richter, Reinhard; Tobiska, Lutz 2 2007 Analysis of a new stabilized higher order finite element method for advection-diffusion equations. Zbl 1120.76336Tobiska, Lutz 20 2006 Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122Lin, Qun; Tobiska, Lutz; Zhou, Aihui 99 2005 Convergence analysis of a multiscale finite element method for singularly perturbed problems. Zbl 1091.65108Franca, Leopoldo P.; Madureira, Alexandre L.; Tobiska, Lutz; Valentin, Frédéric 15 2005 Inf-sup stable nonconforming finite elements of arbitrary order on triangles. Zbl 1089.65123Matthies, Gunar; Tobiska, Lutz 10 2005 Superconvergence of a 3D finite element method for stationary Stokes and Navier-Stokes problems. Zbl 1078.65091Matthies, G.; Skrzypacz, P.; Tobiska, L. 6 2005 On Korn’s first inequality for quadrilateral nonconforming finite elements of first-order approximation properties. Zbl 1106.65096Knobloch, Petr; Tobiska, Lutz 3 2005 Finite element simulation of a droplet impinging a horizontal surface. Zbl 1402.76071Ganesan, Sashikumaar; Tobiska, Lutz 2 2005 Numerical modeling of the equilibrium shapes of a ferrofluid drop in an external magnetic field. Zbl 1354.76138Lavrova, O.; Matthies, G.; Polevikov, V.; Tobiska, L. 4 2004 Numerical simulation of the flow in magnetic fluid rotary shaft seals. Zbl 1151.76557Mitkova, Teodora; Tobiska, Lutz 1 2004 The SDFEM for a convection-diffusion problem with a boundary layer: Optimal error analysis and enhancement of accuracy. Zbl 1055.65121Stynes, Martin; Tobiska, Lutz 48 2003 A numerical study of a class of LES models. Zbl 1148.76327Iliescu, T.; John, V.; Layton, W. J.; Matthies, G.; Tobiska, L. 16 2003 The \(P_1^{\text{mod}}\)-element: A new nonconforming finite element for convection-diffusion problems. Zbl 1048.65111Knobloch, Petr; Tobiska, Lutz 14 2003 Finite element methods for coupled problems in ferrohydrodynamics. Zbl 1138.76385Lavrova, Olga; Matthies, Gunar; Mitkova, Teodora; Polevikov, Viktor; Tobiska, Lutz 6 2003 The inf-sup condition for the mapped \(Q_k-P_{k-1}^{\text{disc}}\) element in arbitrary space dimensions. Zbl 1016.65073Matthies, G.; Tobiska, L. 22 2002 Non-nested multi-level solvers for finite element discretisations of mixed problems. Zbl 1006.65137John, V.; Knobloch, P.; Matthies, G.; Tobiska, L. 15 2002 Stability of the residual free bubble method for bilinear finite elements on rectangular grids. Zbl 1005.65122Franca, Leopoldo P.; Tobiska, Lutz 11 2002 The streamline-diffusion method for nonconforming \(Q_1^{\text{rot}}\) elements on rectangular tensor-product meshes. Zbl 0980.65125Stynes, Martin; Tobiska, Lutz 15 2001 Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers. Zbl 0986.65109Stynes, M.; Tobiska, L. 8 2001 The streamline-diffusion method for conforming and nonconforming finite elements of lowest order applied to convection-diffusion problems. Zbl 0998.65118Matthies, G.; Tobiska, L. 8 2001 Modeling of a dynamic magneto-fluid seal in the presence of a pressure drop. Zbl 1175.76113Polevikov, V. K.; Tobiska, L. 1 2001 Simulation of free surfaces of magnetic liquids. Zbl 1057.76549Matthies, Gunar; Tobiska, Lutz 1 2001 Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier-Stokes equations. Zbl 0979.76047John, Volker; Tobiska, Lutz 17 2000 The convergence of the cascadic conjugate-gradient method applied to elliptic problems in domains with re-entrant corners. Zbl 0947.65037Shaidurov, Vladimir; Tobiska, Lutz 12 2000 A coupled multigrid method for nonconforming finite element discretizations of the 2D-Stokes equation. Zbl 0963.65126John, V.; Tobiska, L. 4 2000 Stabilization methods of bubble type for the \(Q_1/Q_1\)-element applied to the incompressible Navier-Stokes equations. Zbl 0984.76047Knobloch, Petr; Tobiska, Lutz 4 2000 Modified FE discretizations of incompressible flow problems and their relationship to stabilized methods. Zbl 1006.76057Knobloch, Petr; Tobiska, Lutz 1 2000 A comparison of three solvers for the incompressible Navier-Stokes equations. Zbl 0985.76053John, V.; Matthies, G.; Mitkova, T. I.; Tobiska, L.; Vassilevski, P. S. 1 2000 A streamline diffusion method for nonconforming finite element approximations applied to the linearized incompressible Navier-Stokes equation. Zbl 1119.76352Knobloch, P.; Tobiska, L. 2 1999 A two-level method with backtracking for the Navier-Stokes equations. Zbl 0913.76050Layton, W.; Tobiska, L. 102 1998 A finite difference analysis of a streamline diffusion method on a Shishkin mesh. Zbl 0916.65108Stynes, Martin; Tobiska, Lutz 29 1998 A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems. Zbl 0942.76041John, V.; Matthies, G.; Schieweck, F.; Tobiska, L. 21 1998 Analysis of a mathematical model related to Czochralski crystal growth. Zbl 0969.35107Knobloch, Petr; Tobiska, Lutz 1 1998 Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems. Zbl 0898.65068John, V.; Maubach, J. M.; Tobiska, L. 30 1997 Streamline diffusion least-squares mixed finite element methods for convection-diffusion problems. Zbl 0895.65049Lazarov, R. D.; Tobiska, L.; Vassilevski, P. S. 8 1997 Error estimates and numerical experiments for streamline-diffusion-type methods on arbitrary and Shishkin meshes. Zbl 0908.65069Stynes, Martin; Tobiska, Lutz 2 1997 Numerical methods for singularly perturbed differential equations. Convection-diffusion and flow problems. Zbl 0844.65075Roos, Hans-Görg; Stynes, Martin; Tobiska, Lutz 442 1996 Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations. Zbl 0843.76052Tobiska, Lutz; Verfürth, Rüdiger 54 1996 An optimal order error estimate for an upwind discretization of the Navier-Stokes equations. Zbl 0856.76037Schieweck, F.; Tobiska, L. 11 1996 Parallel finite element methods for the incompressible Navier-Stokes equations. Zbl 0876.76039Dorok, O.; John, V.; Risch, U.; Schieweck, F.; Tobiska, L. 4 1996 Necessary \(L^ 2\)-uniform convergence conditions for difference schemes for two-dimensional convection-diffusion problems. Zbl 0822.65077Stynes, M.; Tobiska, L. 12 1995 Special integration formulae for a convection-diffusion problem. Zbl 0839.65117Shaidurov, V.; Tobiska, L. 1 1995 Aspects of finite element discretizations for solving the Boussinesq approximation of the Navier-Stokes equations. Zbl 0876.76038Dorok, O.; Grambow, W.; Tobiska, L. 15 1994 Stabilized finite element methods for the Navier-Stokes problem. Zbl 0793.76053Tobiska, Lutz 3 1993 Finite element method. An introduction. 3., überarb. u. erw. Aufl. Zbl 0780.65066Goering, Herbert; Roos, Hans-Görg; Tobiska, Lutz 2 1993 A modified streamline diffusion method for solving the stationary Navier- Stokes equation. Zbl 0696.76034Tobiska, Lutz; Lube, Gert 17 1991 Finite element methods of streamline diffusion type for the Navier-Stokes equations. Zbl 0744.76080Tobiska, L. 1 1991 A nonconforming finite element method of streamline diffusion type for the incompressible Navier-Stokes equations. Zbl 0699.76032Lube, G.; Tobiska, L. 10 1990 A nonconforming finite element method of upstream type applied to the stationary Navier-Stokes equation. Zbl 0681.76032Schieweck, F.; Tobiska, L. 16 1989 Full and weighted upwind finite element methods. Zbl 0685.65074Tobiska, Lutz 7 1989 Eine upwind FEM zur Lösung des stationären Navier-Stokes Problems. (An upwind FEM for the solution of the stationary Navier-Stokes problem). Zbl 0638.76032Schieweck, Friedhelm; Tobiska, Lutz 1 1987 An enclosure generating modification of the method of discretization in time. Zbl 0635.65122Koeppe, G.; Roos, H.-G.; Tobiska, L. 1 1987 Singularly perturbed differential equations. Zbl 0522.35003Goering, Herbert; Felgenhauer, Andreas; Lube, Gert; Roos, Hans-Goerg; Tobiska, Lutz 16 1983 Diskretisierungsverfahren zur Lösung singulär gestörter Randwertprobleme. Zbl 0535.65058Tobiska, L. 3 1983 Die asymptotische Lösung singulär gestörter elliptischer Probleme 2. Ordnung. Zbl 0479.35009Tobiska, Lutz; Lube, Gert 1 1980 Asymptotische Lösung singulär gestörter Probleme. Zbl 0421.35005Tobiska, Lutz 1 1978 all cited Publications top 5 cited Publications all top 5 Cited by 1,661 Authors 55 Shi, Dongyang 44 John, Volker 40 Tobiska, Lutz 32 Stynes, Martin 31 He, Yinnian 31 Roos, Hans-Görg 29 Matthies, Gunar 27 Linke, Alexander 27 Lube, Gert 25 Natesan, Srinivasan 24 Shishkin, Grigoriĭ Ivanovich 21 Kadalbajoo, Mohan K. 20 Franz, Sebastian 20 Linß, Torsten 19 Amiraliyev, Gabil M. 19 Clavero, Carmelo 19 O’Riordan, Eugene 17 Gracia, José Luis 17 Knobloch, Petr 16 Burman, Erik 16 Liu, Xiaowei 16 Ramanujam, Narashimhan 16 Zhang, Jin 15 Ahmed, Naveed 15 Ganesan, Sashikumaar 15 Schieweck, Friedhelm 13 Feng, Minfu 13 Layton, William J. 13 Rebholz, Leo G. 13 Xenophontos, Christos A. 12 Kaushik, Aditya 12 Novo, Julia 11 Feng, Xinlong 11 Kopteva, Natalia Viktorovna 11 Li, Jichun 11 Valentin, Frédéric 10 Barrenechea, Gabriel R. 10 Kumar, Sunil 10 Patidar, Kailash C. 10 Teofanov, Ljiljana 10 Xie, Hehu 9 Cen, Zhongdi 9 Feistauer, Miloslav 9 Garcke, Harald 9 Hu, Jun 9 Huang, Pengzhan 9 Jung, Changyeol 9 Lisbona Cortés, Francisco Javier 9 Merdon, Christian 9 Miller, John James Henry 9 Sacco, Riccardo 9 Shanthi, V. G. 9 Turek, Stefan 9 Zarin, Helena 9 Zhu, Peng 8 Araya, Rodolfo A. 8 Chen, Shaochun 8 Codina, Ramon 8 Guan, Hongbo 8 Kumar, Mukesh 8 Lin, Qun 8 Madden, Niall 8 Mao, Shipeng 8 Nesliturk, Ali I. 8 Rao, S. Chandra Sekhara 8 Sharma, Kapil Kumar 8 Temam, Roger Meyer 8 Wang, Song 7 Braack, Malte 7 Chacón Rebollo, Tomás 7 de Frutos, Javier 7 Erdogan, Fevzi 7 Ern, Alexandre 7 Jorge, Juan Carlos 7 Ramanujam, Narasimhan 7 Shi, Zhongci 7 Xu, Jinchao 7 Zhang, Zhimin 7 Zhao, Yanmin 6 Allendes, Alejandro 6 Bawa, Rajesh Kumar 6 Fernández, Miguel Ángel 6 Franca, Leopoldo Luis Cabo Penna 6 Fuhrmann, Jürgen 6 Kellogg, Bruce 6 Kumar, Devendra 6 Li, Zi-Cai 6 Nürnberg, Robert 6 Olshanskii, Maxim A. 6 Reusken, Arnold 6 Schroeder, Philipp W. 6 Shang, Yueqiang 6 Sun, Pengtao 6 Tamilselvan, Ayyadurai 6 Valarmathi, Sigamani 6 Vulanović, Relja 6 Zhang, Yan 5 Arndt, Daniel 5 Barrett, John W. 5 Buscaglia, Gustavo C. ...and 1,561 more Authors all top 5 Cited in 152 Serials 145 Computer Methods in Applied Mechanics and Engineering 128 Applied Mathematics and Computation 122 Journal of Computational and Applied Mathematics 83 Computers & Mathematics with Applications 81 Applied Numerical Mathematics 71 Journal of Computational Physics 50 Journal of Scientific Computing 42 Mathematics of Computation 40 Numerical Algorithms 31 Computers and Fluids 31 Advances in Computational Mathematics 30 Numerische Mathematik 25 Numerical Methods for Partial Differential Equations 21 SIAM Journal on Numerical Analysis 21 Applied Mathematics Letters 20 Journal of Mathematical Analysis and Applications 19 Computing 17 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 15 Applied Mathematics and Mechanics. (English Edition) 14 International Journal for Numerical Methods in Fluids 14 BIT 14 Calcolo 14 International Journal of Computer Mathematics 12 Applications of Mathematics 11 Applied Mathematical Modelling 10 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 10 Journal of Numerical Mathematics 10 Science China. Mathematics 9 SIAM Journal on Scientific Computing 9 Communications in Nonlinear Science and Numerical Simulation 9 Computational Methods in Applied Mathematics 8 Journal of Fluid Mechanics 8 Numerical Functional Analysis and Optimization 8 International Journal of Applied and Computational Mathematics 7 International Journal for Numerical Methods in Engineering 7 Computational and Applied Mathematics 7 Engineering Analysis with Boundary Elements 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 6 Mathematical Methods in the Applied Sciences 6 Journal of Optimization Theory and Applications 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Acta Mathematicae Applicatae Sinica. English Series 6 Abstract and Applied Analysis 6 Journal of Systems Science and Complexity 6 Journal of Applied Mathematics and Computing 6 Advances in Difference Equations 5 Journal of Engineering Mathematics 5 Mathematical and Computer Modelling 5 Differential Equations and Dynamical Systems 5 International Journal of Computational Methods 5 S\(\vec{\text{e}}\)MA Journal 4 Mathematics and Computers in Simulation 4 Computational Mechanics 4 Computing and Visualization in Science 4 Journal of Mathematical Fluid Mechanics 4 Archives of Computational Methods in Engineering 3 Computer Physics Communications 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 Zeitschrift für Analysis und ihre Anwendungen 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Science in China. Series A 3 Japan Journal of Industrial and Applied Mathematics 3 Computational Mathematics and Mathematical Physics 3 Communications in Numerical Methods in Engineering 3 Numerical Linear Algebra with Applications 3 ETNA. Electronic Transactions on Numerical Analysis 3 Journal of Difference Equations and Applications 3 Mathematical Problems in Engineering 3 International Journal of Computational Fluid Dynamics 3 Taiwanese Journal of Mathematics 3 European Journal of Mechanics. B. Fluids 3 Nonlinear Analysis. Real World Applications 3 Journal of Applied Mathematics 3 Multiscale Modeling & Simulation 3 Proceedings of the Steklov Institute of Mathematics 3 Advances in Numerical Analysis 3 Journal of Applied Mathematics & Informatics 3 Electronic Research Archive 2 Applicable Analysis 2 Kybernetika 2 Acta Applicandae Mathematicae 2 SIAM Review 2 Cybernetics and Systems Analysis 2 Physics of Fluids 2 Journal of the Egyptian Mathematical Society 2 Turkish Journal of Mathematics 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Combustion Theory and Modelling 2 Foundations of Computational Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Central European Journal of Mathematics 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Frontiers of Mathematics in China 2 International Journal for Computational Methods in Engineering Science and Mechanics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 2 SMAI Journal of Computational Mathematics 1 Acta Mechanica 1 International Journal of Heat and Mass Transfer 1 Indian Journal of Pure & Applied Mathematics ...and 52 more Serials all top 5 Cited in 29 Fields 1,202 Numerical analysis (65-XX) 576 Fluid mechanics (76-XX) 510 Partial differential equations (35-XX) 189 Ordinary differential equations (34-XX) 47 Mechanics of deformable solids (74-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 20 Classical thermodynamics, heat transfer (80-XX) 19 Biology and other natural sciences (92-XX) 17 Statistical mechanics, structure of matter (82-XX) 12 Optics, electromagnetic theory (78-XX) 11 Integral equations (45-XX) 8 Approximations and expansions (41-XX) 8 Computer science (68-XX) 6 Geophysics (86-XX) 5 Real functions (26-XX) 5 Systems theory; control (93-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 2 History and biography (01-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year