Edit Profile (opens in new tab) Rebholz, Leo G. Compute Distance To: Compute Author ID: rebholz.leo-g Published as: Rebholz, Leo G.; Rebholz, Leo; Rebholz, L. G.; Rebholz, L. Documents Indexed: 112 Publications since 2006, including 3 Books Co-Authors: 83 Co-Authors with 106 Joint Publications 1,625 Co-Co-Authors all top 5 Co-Authors 6 single-authored 14 Olshanskii, Maxim A. 13 Neda, Monika 12 Linke, Alexander 11 Layton, William J. 11 Manica, Carolina Cardoso 11 Xiao, Mengying 8 Heister, Timo 8 Kaya, Songul 8 Mohebujjaman, Muhammad 8 Wilson, Nicholas E. 7 Akbas, Mine 6 Bowers, Abigail L. 6 Kim, Tae-Yeon 6 Zerfas, Camille 5 Iliescu, Traian 5 Trenchea, Catalin 4 Fried, Eliot 4 Galvin, Keith J. 4 Larios, Adam 4 Pollock, Sara 3 Belenli, Mine Akbas 3 Cousins, Benjamin R. 3 Dunca, Argus Adrian 3 Le Borne, Sabine 2 Case, Michael A. 2 Charnyi, Sergey 2 Eroglu, Fatma G. 2 Ervin, Vincent J. 2 Jenkins, Eleanor W. 2 John, Volker 2 Labovsky, Alexandr 2 Lee, Hyesuk Kwon 2 Morales Hernandez, Monica 2 Neilan, Michael 2 Sussman, Myron M. 2 Tone, Florentina 2 Vargun, Duygu 2 Viguerie, Alex 2 Wang, Zhen 2 Xie, Xuping 2 Zhao, Kun 1 Al Mahbub, Md. Abdullah 1 Benzi, Michele 1 Berselli, Luigi Carlo 1 Bertagna, Luca 1 Byon, Young-Ji 1 Cao, Yanzhao 1 Chen, Song 1 Connors, Jeffrey Mark 1 Cuff, Victoria M. 1 D’Agnillo, Erica M. 1 Diegel, Amanda E. 1 Evans, Claire 1 Forbes, Dominique 1 Gardner, Matthew 1 Gerritsma, Marc I. 1 Jiang, Nan 1 Koc, Birgul 1 Kohler, Kara E. 1 Kuberry, Paul Allen 1 Labovschii, A. 1 Merdon, Christian 1 Miles, William W. 1 Monteiro, Igor Olivia 1 Mou, Changhong 1 Pahlevani, Faranak 1 Palha, Artur 1 Pei, Yuan 1 Pruett, C. David 1 Quaini, Annalisa 1 Salgado, Abner J. 1 San, Omer 1 Schneier, Michael 1 Schroeder, Philipp W. 1 Stanculescu, Iuliana 1 Takhirov, Aziz 1 Tone, Cristina 1 Veneziani, Alessandro 1 Wang, Dehua 1 Wang, Zhian 1 Waters, Jiajia Wang 1 Watro, Stacey A. 1 Wise, Steven M. all top 5 Serials 19 Computer Methods in Applied Mechanics and Engineering 8 Journal of Computational Physics 7 Numerical Methods for Partial Differential Equations 6 Journal of Mathematical Analysis and Applications 6 Applied Mathematics and Computation 6 SIAM Journal on Numerical Analysis 4 Journal of Numerical Mathematics 4 International Journal of Numerical Analysis and Modeling 3 Computers & Mathematics with Applications 3 Computational Methods in Applied Mathematics 2 Mathematical Methods in the Applied Sciences 2 Journal of Computational and Applied Mathematics 2 Applied Mathematical Modelling 2 International Journal of Computer Mathematics 2 SIAM Journal on Scientific Computing 2 Discrete and Continuous Dynamical Systems 2 Journal of Mathematical Fluid Mechanics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 IMA Journal of Applied Mathematics 1 IMA Journal of Numerical Analysis 1 International Journal for Numerical Methods in Fluids 1 Mathematics of Computation 1 Calcolo 1 Journal of Differential Equations 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Review 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Computing and Visualization in Science 1 International Journal of Computational Fluid Dynamics 1 Discrete and Continuous Dynamical Systems. Series B 1 Lecture Notes in Mathematics 1 Advances and Applications in Fluid Mechanics 1 Advances in Numerical Analysis 1 Advances in Applied Mathematics and Mechanics 1 International Journal of Numerical Analysis and Modeling. Series B 1 Journal of Nonlinear Dynamics 1 De Gruyter Textbook 1 De Gruyter Graduate 1 Electronic Research Archive all top 5 Fields 96 Fluid mechanics (76-XX) 72 Numerical analysis (65-XX) 38 Partial differential equations (35-XX) 4 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 90 Publications have been cited 1,199 times in 514 Documents Cited by ▼ Year ▼ On the divergence constraint in mixed finite element methods for incompressible flows. Zbl 1426.76275John, Volker; Linke, Alexander; Merdon, Christian; Neilan, Michael; Rebholz, Leo G. 118 2017 On the accuracy of the rotation form in simulations of the Navier-Stokes equations. Zbl 1161.76030Layton, William; Manica, Carolina C.; Neda, Monika; Olshanskii, Maxim; Rebholz, Leo G. 59 2008 A connection between Scott-Vogelius and grad-div stabilized Taylor-Hood FE approximations of the Navier-Stokes equations. Zbl 1244.76021Case, Michael A.; Ervin, Vincent J.; Linke, Alexander; Rebholz, Leo G. 58 2011 Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence. Zbl 1191.76061Layton, William; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 54 2008 Approximate deconvolution models of turbulence. Analysis, phenomenology and numerical analysis. Zbl 1241.76002Layton, William J.; Rebholz, Leo 51 2012 On the parameter choice in grad-div stabilization for the Stokes equations. Zbl 1426.76272Jenkins, Eleanor W.; John, Volker; Linke, Alexander; Rebholz, Leo G. 49 2014 The stabilized extrapolated trapezoidal finite element method for the Navier-Stokes equations. Zbl 1229.76051Labovsky, Alexandr; Layton, William J.; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 39 2009 Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection. Zbl 1253.76057Galvin, Keith J.; Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E. 38 2012 Data-driven filtered reduced order modeling of fluid flows. Zbl 1412.65158Xie, X.; Mohebujjaman, M.; Rebholz, L. G.; Iliescu, T. 29 2018 Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations. Zbl 1406.76031Layton, William; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 29 2010 On conservation laws of Navier-Stokes Galerkin discretizations. Zbl 1415.65222Charnyi, Sergey; Heister, Timo; Olshanskii, Maxim A.; Rebholz, Leo G. 26 2017 Conservation laws of turbulence models. Zbl 1110.76028Rebholz, Leo G. 26 2007 On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems. Zbl 1331.76038Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E. 25 2011 Enabling numerical accuracy of Navier-Stokes-\(\alpha\) through deconvolution and enhanced stability. Zbl 1267.76021Manica, Carolina C.; Neda, Monika; Olshanskii, Maxim; Rebholz, Leo G. 23 2011 Energy balance and mass conservation in reduced-order models of fluid flows. Zbl 1378.76050Mohebujjaman, Muhammad; Rebholz, Leo G.; Xie, Xuping; Iliescu, Traian 20 2017 Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations. Zbl 1334.76083Olshanskii, Maxim A.; Rebholz, Leo G. 20 2010 Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations. Zbl 1387.76052Heister, Timo; Olshanskii, Maxim A.; Rebholz, Leo G. 18 2017 Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows. Zbl 1268.76014Kuberry, Paul; Larios, Adam; Rebholz, Leo G.; Wilson, Nicholas E. 17 2012 A family of new, high order NS-\(\alpha \) models arising from helicity correction in Leray turbulence models. Zbl 1138.35078Rebholz, Leo G. 17 2008 An energy- and helicity-conserving finite element scheme for the Navier-Stokes equations. Zbl 1141.76039Rebholz, Leo G. 16 2007 Modular nonlinear filter stabilization of methods for higher Reynolds numbers flow. Zbl 1294.76197Layton, William; Rebholz, Leo G.; Trenchea, Catalin 16 2012 On error analysis for the 3D Navier-Stokes equations in velocity-vorticity-helicity form. Zbl 1222.35143Lee, Hyesuk K.; Olshanskii, Maxim A.; Rebholz, Leo G. 14 2011 An efficient algorithm for computation of MHD flow ensembles. Zbl 1419.76443Mohebujjaman, Muhammad; Rebholz, Leo G. 14 2017 A proof that Anderson acceleration improves the convergence rate in linearly converging fixed-point methods (but not in those converging quadratically). Zbl 1433.65102Evans, Claire; Pollock, Sara; Rebholz, Leo G.; Xiao, Mengying 14 2020 Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization. Zbl 1296.76079Bowers, Abigail L.; Le Borne, Sabine; Rebholz, Leo G. 13 2014 Increasing accuracy and efficiency in FE computations of the Leray-deconvolution model. Zbl 1414.76035Bowers, Abigail L.; Rebholz, Leo G. 13 2012 Decoupled, unconditionally stable, higher order discretizations for MHD flow simulation. Zbl 06849348Heister, Timo; Mohebujjaman, Muhammad; Rebholz, Leo G. 12 2017 Numerical study of a regularization model for incompressible flow with deconvolution-based adaptive nonlinear filtering. Zbl 1286.76079Bowers, Abigail L.; Rebholz, Leo G. 12 2013 Numerical analysis and testing of a fully discrete, decoupled penalty-projection algorithm for MHD in Elsässer variable. Zbl 1345.76114Akbas, Mine; Kaya, Songul; Mohebujjaman, Muhammad; Rebholz, Leo G. 12 2016 Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization. Zbl 1346.35157Berselli, Luigi C.; Kim, Tae-Yeon; Rebholz, Leo G. 12 2016 On a reduced sparsity stabilization of Grad-div type for incompressible flow problems. Zbl 1286.76032Linke, Alexander; Rebholz, Leo G. 11 2013 Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models. Zbl 1385.76010Galvin, Keith J.; Rebholz, Leo G.; Trenchea, Catalin 11 2014 On the high accuracy NS-alpha-deconvolution turbulence model. Zbl 1187.76720Rebholz, Leo G.; Sussman, Myron M. 10 2010 On an efficient finite element method for Navier-Stokes-\(\overline{\omega}\) with strong mass conservation. Zbl 1283.76018Manica, Carolina C.; Neda, Monika; Olshanskii, Maxim; Rebholz, Leo G.; Wilson, Nicholas E. 10 2011 An enhanced-physics-based scheme for the NS-\(\alpha \) turbulence model. Zbl 1426.76191Miles, William W.; Rebholz, Leo G. 10 2010 On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems. Zbl 1439.76043Akbas, M.; Kaya, S.; Rebholz, L. G. 10 2017 Improved accuracy in algebraic splitting methods for Navier-Stokes equations. Zbl 1420.35198Rebholz, Leo G.; Xiao, Mengying 10 2017 Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier-Stokes equations. Zbl 1440.76075Larios, Adam; Rebholz, Leo G.; Zerfas, Camille 10 2019 A subgrid stabilization finite element method for incompressible magnetohydrodynamics. Zbl 1452.76265Belenli, Mine A.; Kaya, Songül; Rebholz, Leo G.; Wilson, Nicholas E. 9 2013 A numerical study of the Navier-Stokes-\(\alpha \beta \) model. Zbl 1230.76027Kim, Tae-Yeon; Neda, Monika; Rebholz, Leo G.; Fried, Eliot 9 2011 Helicity and energy conservation and dissipation in approximate deconvolution LES models of turbulence. Zbl 1176.76046Layton, William J.; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 9 2008 A deconvolution enhancement of the Navier-Stokes-\({\alpha}{\beta}\) model. Zbl 1404.76140Kim, Tae-Yeon; Rebholz, Leo G.; Fried, Eliot 9 2012 Energy and helicity dissipation rates of the NS-alpha and NS-alpha-deconvolution models. Zbl 1423.76160Layton, William; Rebholz, Leo; Sussman, Myron 9 2010 Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions. Zbl 07069017Rebholz, Leo G.; Wang, Dehua; Wang, Zhian; Zerfas, Camille; Zhao, Kun 8 2019 Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements. Zbl 1312.76025Cousins, Benjamin R.; Le Borne, Sabine; Linke, Alexander; Rebholz, Leo G.; Wang, Zhen 8 2013 A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations. Zbl 1453.65331Linke, Alexander; Neilan, Michael; Rebholz, Leo G.; Wilson, Nicholas E. 8 2017 A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements. Zbl 1311.76044Belenli, Mine Akbas; Rebholz, Leo G.; Tone, Florentina 8 2015 Application of barycenter refined meshes in linear elasticity and incompressible fluid dynamics. Zbl 1426.74302Olshanskii, Maxim A.; Rebholz, Leo G. 8 2011 Continuous data assimilation reduced order models of fluid flow. Zbl 1442.65006Zerfas, Camille; Rebholz, Leo G.; Schneier, Michael; Iliescu, Traian 8 2019 Natural vorticity boundary conditions on solid walls. Zbl 1423.76100Olshanskii, Maxim A.; Heister, Timo; Rebholz, Leo G.; Galvin, Keith J. 7 2015 Anderson-accelerated convergence of Picard iterations for incompressible Navier-Stokes equations. Zbl 1412.65198Pollock, Sara; Rebholz, Leo G.; Xiao, Mengying 7 2019 The reduced order NS-\(\alpha\) model for incompressible flow: theory, numerical analysis and benchmark testing. Zbl 1321.76032Cuff, Victoria M.; Dunca, Argus A.; Manica, Carolina C.; Rebholz, Leo G. 7 2015 An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations. Zbl 1439.76076Jiang, Nan; Mohebujjaman, Muhammad; Rebholz, Leo G.; Trenchea, Catalin 7 2016 Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering. Zbl 1412.76044Bowers, A. L.; Rebholz, L. G.; Takhirov, A.; Trenchea, C. 6 2012 Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations. Zbl 1432.76077Cousins, Benjamin R.; Rebholz, Leo G.; Wilson, Nicholas E. 6 2011 Note on helicity balance of the Galerkin method for the 3D Navier-Stokes equations. Zbl 1227.76037Olshanskii, Maxim; Rebholz, Leo G. 6 2010 On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions. Zbl 1338.76086Kaya, Songul; Manica, Carolina C.; Rebholz, Leo G. 6 2014 An explicitly decoupled variational multiscale method for incompressible, non-isothermal flows. Zbl 1309.76122Belenli, Mine A.; Kaya, Songül; Rebholz, Leo G. 5 2015 On well-posedness of a velocity-vorticity formulation of the stationary Navier-Stokes equations with no-slip boundary conditions. Zbl 1397.35178Olshanskii, Maxim A.; Rebholz, Leo G.; Salgado, Abner J. 5 2018 On reducing the splitting error in Yosida methods for the Navier-Stokes equations with Grad-div stabilization. Zbl 1423.76270Rebholz, Leo G.; Xiao, Mengying 5 2015 The Leray-\(\alpha\beta\)-deconvolution model: energy analysis and numerical algorithms. Zbl 1351.76049Bowers, Abigail L.; Kim, Tae-Yeon; Neda, Monika; Rebholz, Leo G.; Fried, Eliot 5 2013 Assessment of a vorticity based solver for the Navier-Stokes equations. Zbl 1352.76040Benzi, Michele; Olshanskii, Maxim A.; Rebholz, Leo G.; Wang, Zhen 5 2012 Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems. Zbl 1376.65034Le Borne, Sabine; Rebholz, Leo G. 5 2013 Efficient discretizations for the EMAC formulation of the incompressible Navier-Stokes equations. Zbl 1478.65082Charnyi, Sergey; Heister, Timo; Olshanskii, Maxim A.; Rebholz, Leo G. 4 2019 Penalty projection schemes for the Cahn-Hilliard Navier-Stokes diffuse interface model of two phase flow, and their connection to divergence-free coupled schemes. Zbl 1395.35109Rebholz, Leo G.; Wise, Steven M.; Xiao, Mengying 4 2018 Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations. Zbl 1452.76092Linke, Alexander; Rebholz, Leo G. 4 2019 Temporally regularized direct numerical simulation. Zbl 1339.76037Layton, William J.; Pruett, C. David; Rebholz, Leo G. 4 2010 Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow. Zbl 1462.65154Neda, Monika; Pahlevani, Faranak; Rebholz, Leo G.; Waters, Jiajia 4 2016 A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows. Zbl 1439.76065Eroglu, Fatma G.; Kaya, Songul; Rebholz, Leo G. 4 2017 The analogue of grad-div stabilization in DG methods for incompressible flows: limiting behavior and extension to tensor-product meshes. Zbl 1440.76047Akbas, Mine; Linke, Alexander; Rebholz, Leo G.; Schroeder, Philipp W. 4 2018 Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation. Zbl 07337865Olshanskii, Maxim A.; Rebholz, Leo G. 4 2020 Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. Zbl 1468.65141Gardner, Matthew; Larios, Adam; Rebholz, Leo G.; Vargun, Duygu; Zerfas, Camille 4 2021 Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations. Zbl 1433.35235Larios, Adam; Pei, Yuan; Rebholz, Leo 3 2019 Well-posedness of a reduced order approximate deconvolution turbulence model. Zbl 1306.35099Rebholz, Leo G. 3 2013 Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations. Zbl 1450.65114Akbas, M.; Rebholz, L. G.; Zerfas, C. 3 2018 New connections between finite element formulations of the Navier-Stokes equations. Zbl 1427.76120Bowers, Abigail L.; Cousins, Benjamin R.; Linke, Alexander; Rebholz, Leo G. 3 2010 A mathematical and physical study of multiscale deconvolution models of turbulence. Zbl 1247.35089Dunca, Argus Adrian; Kohler, Kara E.; Neda, Monika; Rebholz, Leo G. 3 2012 Stable computing with an enhanced physics based scheme for the 3D Navier-Stokes equations. Zbl 1429.76069Case, Michael A.; Ervin, Vincent J.; Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E. 3 2011 Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations. Zbl 1416.65421Rebholz, Leo G.; Viguerie, Alex; Xiao, Mengying 3 2019 POD-ROM for the Darcy-Brinkman equations with double-diffusive convection. Zbl 1458.65125Eroglu, Fatma G.; Kaya, Songul; Rebholz, Leo G. 3 2019 Global in time analysis and sensitivity analysis for the reduced NS-\(\alpha\) model of incompressible flow. Zbl 1402.35229Rebholz, Leo; Zerfas, Camille; Zhao, Kun 3 2017 Data-driven variational multiscale reduced order models. Zbl 07337754Mou, Changhong; Koc, Birgul; San, Omer; Rebholz, Leo G.; Iliescu, Traian 3 2021 Small-scale divergence penalization for incompressible flow problems via time relaxation. Zbl 1381.76159Connors, Jeffrey M.; Jenkins, Eleanor W.; Rebholz, Leo G. 2 2011 On an accurate \(\alpha\) model for coarse mesh turbulent channel flow simulation. Zbl 1446.76039Rebholz, Leo G.; Kim, Tae-Yeon; Byon, Young-Ji 2 2017 Flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for strongly divergence-free mixed finite element methods for flow problems. Zbl 1382.35223Heister, Timo; Rebholz, Leo G.; Xiao, Mengying 2 2016 Stability of the Crank-Nicolson-Adams-Bashforth scheme for the 2D Leray-\(\alpha\) model. Zbl 1382.65277Morales Hernandez, Monica; Rebholz, Leo G.; Tone, Cristina; Tone, Florentina 2 2016 On the sensitivity to the filtering radius in Leray models of incompressible flow. Zbl 1418.35300Bertagna, Luca; Quaini, Annalisa; Rebholz, Leo G.; Veneziani, Alessandro 1 2019 A note on helicity conservation in Leray models of incompressible flow. Zbl 1304.35500Morales Hernandez, Monica; Rebholz, Leo G. 1 2015 On the enforcement of discrete mass conservation in incompressible flow simulations with continuous velocity approximation. Zbl 1287.76165D’Agnillo, Erica M.; Rebholz, Leo G. 1 2013 A multiscale V-P discretization for flow problems. Zbl 1091.76037Rebholz, Leo G. 1 2006 Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. Zbl 1468.65141Gardner, Matthew; Larios, Adam; Rebholz, Leo G.; Vargun, Duygu; Zerfas, Camille 4 2021 Data-driven variational multiscale reduced order models. Zbl 07337754Mou, Changhong; Koc, Birgul; San, Omer; Rebholz, Leo G.; Iliescu, Traian 3 2021 A proof that Anderson acceleration improves the convergence rate in linearly converging fixed-point methods (but not in those converging quadratically). Zbl 1433.65102Evans, Claire; Pollock, Sara; Rebholz, Leo G.; Xiao, Mengying 14 2020 Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation. Zbl 07337865Olshanskii, Maxim A.; Rebholz, Leo G. 4 2020 Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier-Stokes equations. Zbl 1440.76075Larios, Adam; Rebholz, Leo G.; Zerfas, Camille 10 2019 Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions. Zbl 07069017Rebholz, Leo G.; Wang, Dehua; Wang, Zhian; Zerfas, Camille; Zhao, Kun 8 2019 Continuous data assimilation reduced order models of fluid flow. Zbl 1442.65006Zerfas, Camille; Rebholz, Leo G.; Schneier, Michael; Iliescu, Traian 8 2019 Anderson-accelerated convergence of Picard iterations for incompressible Navier-Stokes equations. Zbl 1412.65198Pollock, Sara; Rebholz, Leo G.; Xiao, Mengying 7 2019 Efficient discretizations for the EMAC formulation of the incompressible Navier-Stokes equations. Zbl 1478.65082Charnyi, Sergey; Heister, Timo; Olshanskii, Maxim A.; Rebholz, Leo G. 4 2019 Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations. Zbl 1452.76092Linke, Alexander; Rebholz, Leo G. 4 2019 Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations. Zbl 1433.35235Larios, Adam; Pei, Yuan; Rebholz, Leo 3 2019 Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations. Zbl 1416.65421Rebholz, Leo G.; Viguerie, Alex; Xiao, Mengying 3 2019 POD-ROM for the Darcy-Brinkman equations with double-diffusive convection. Zbl 1458.65125Eroglu, Fatma G.; Kaya, Songul; Rebholz, Leo G. 3 2019 On the sensitivity to the filtering radius in Leray models of incompressible flow. Zbl 1418.35300Bertagna, Luca; Quaini, Annalisa; Rebholz, Leo G.; Veneziani, Alessandro 1 2019 Data-driven filtered reduced order modeling of fluid flows. Zbl 1412.65158Xie, X.; Mohebujjaman, M.; Rebholz, L. G.; Iliescu, T. 29 2018 On well-posedness of a velocity-vorticity formulation of the stationary Navier-Stokes equations with no-slip boundary conditions. Zbl 1397.35178Olshanskii, Maxim A.; Rebholz, Leo G.; Salgado, Abner J. 5 2018 Penalty projection schemes for the Cahn-Hilliard Navier-Stokes diffuse interface model of two phase flow, and their connection to divergence-free coupled schemes. Zbl 1395.35109Rebholz, Leo G.; Wise, Steven M.; Xiao, Mengying 4 2018 The analogue of grad-div stabilization in DG methods for incompressible flows: limiting behavior and extension to tensor-product meshes. Zbl 1440.76047Akbas, Mine; Linke, Alexander; Rebholz, Leo G.; Schroeder, Philipp W. 4 2018 Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations. Zbl 1450.65114Akbas, M.; Rebholz, L. G.; Zerfas, C. 3 2018 On the divergence constraint in mixed finite element methods for incompressible flows. Zbl 1426.76275John, Volker; Linke, Alexander; Merdon, Christian; Neilan, Michael; Rebholz, Leo G. 118 2017 On conservation laws of Navier-Stokes Galerkin discretizations. Zbl 1415.65222Charnyi, Sergey; Heister, Timo; Olshanskii, Maxim A.; Rebholz, Leo G. 26 2017 Energy balance and mass conservation in reduced-order models of fluid flows. Zbl 1378.76050Mohebujjaman, Muhammad; Rebholz, Leo G.; Xie, Xuping; Iliescu, Traian 20 2017 Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations. Zbl 1387.76052Heister, Timo; Olshanskii, Maxim A.; Rebholz, Leo G. 18 2017 An efficient algorithm for computation of MHD flow ensembles. Zbl 1419.76443Mohebujjaman, Muhammad; Rebholz, Leo G. 14 2017 Decoupled, unconditionally stable, higher order discretizations for MHD flow simulation. Zbl 06849348Heister, Timo; Mohebujjaman, Muhammad; Rebholz, Leo G. 12 2017 On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems. Zbl 1439.76043Akbas, M.; Kaya, S.; Rebholz, L. G. 10 2017 Improved accuracy in algebraic splitting methods for Navier-Stokes equations. Zbl 1420.35198Rebholz, Leo G.; Xiao, Mengying 10 2017 A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations. Zbl 1453.65331Linke, Alexander; Neilan, Michael; Rebholz, Leo G.; Wilson, Nicholas E. 8 2017 A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows. Zbl 1439.76065Eroglu, Fatma G.; Kaya, Songul; Rebholz, Leo G. 4 2017 Global in time analysis and sensitivity analysis for the reduced NS-\(\alpha\) model of incompressible flow. Zbl 1402.35229Rebholz, Leo; Zerfas, Camille; Zhao, Kun 3 2017 On an accurate \(\alpha\) model for coarse mesh turbulent channel flow simulation. Zbl 1446.76039Rebholz, Leo G.; Kim, Tae-Yeon; Byon, Young-Ji 2 2017 Numerical analysis and testing of a fully discrete, decoupled penalty-projection algorithm for MHD in Elsässer variable. Zbl 1345.76114Akbas, Mine; Kaya, Songul; Mohebujjaman, Muhammad; Rebholz, Leo G. 12 2016 Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization. Zbl 1346.35157Berselli, Luigi C.; Kim, Tae-Yeon; Rebholz, Leo G. 12 2016 An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations. Zbl 1439.76076Jiang, Nan; Mohebujjaman, Muhammad; Rebholz, Leo G.; Trenchea, Catalin 7 2016 Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow. Zbl 1462.65154Neda, Monika; Pahlevani, Faranak; Rebholz, Leo G.; Waters, Jiajia 4 2016 Flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for strongly divergence-free mixed finite element methods for flow problems. Zbl 1382.35223Heister, Timo; Rebholz, Leo G.; Xiao, Mengying 2 2016 Stability of the Crank-Nicolson-Adams-Bashforth scheme for the 2D Leray-\(\alpha\) model. Zbl 1382.65277Morales Hernandez, Monica; Rebholz, Leo G.; Tone, Cristina; Tone, Florentina 2 2016 A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements. Zbl 1311.76044Belenli, Mine Akbas; Rebholz, Leo G.; Tone, Florentina 8 2015 Natural vorticity boundary conditions on solid walls. Zbl 1423.76100Olshanskii, Maxim A.; Heister, Timo; Rebholz, Leo G.; Galvin, Keith J. 7 2015 The reduced order NS-\(\alpha\) model for incompressible flow: theory, numerical analysis and benchmark testing. Zbl 1321.76032Cuff, Victoria M.; Dunca, Argus A.; Manica, Carolina C.; Rebholz, Leo G. 7 2015 An explicitly decoupled variational multiscale method for incompressible, non-isothermal flows. Zbl 1309.76122Belenli, Mine A.; Kaya, Songül; Rebholz, Leo G. 5 2015 On reducing the splitting error in Yosida methods for the Navier-Stokes equations with Grad-div stabilization. Zbl 1423.76270Rebholz, Leo G.; Xiao, Mengying 5 2015 A note on helicity conservation in Leray models of incompressible flow. Zbl 1304.35500Morales Hernandez, Monica; Rebholz, Leo G. 1 2015 On the parameter choice in grad-div stabilization for the Stokes equations. Zbl 1426.76272Jenkins, Eleanor W.; John, Volker; Linke, Alexander; Rebholz, Leo G. 49 2014 Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization. Zbl 1296.76079Bowers, Abigail L.; Le Borne, Sabine; Rebholz, Leo G. 13 2014 Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models. Zbl 1385.76010Galvin, Keith J.; Rebholz, Leo G.; Trenchea, Catalin 11 2014 On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions. Zbl 1338.76086Kaya, Songul; Manica, Carolina C.; Rebholz, Leo G. 6 2014 Numerical study of a regularization model for incompressible flow with deconvolution-based adaptive nonlinear filtering. Zbl 1286.76079Bowers, Abigail L.; Rebholz, Leo G. 12 2013 On a reduced sparsity stabilization of Grad-div type for incompressible flow problems. Zbl 1286.76032Linke, Alexander; Rebholz, Leo G. 11 2013 A subgrid stabilization finite element method for incompressible magnetohydrodynamics. Zbl 1452.76265Belenli, Mine A.; Kaya, Songül; Rebholz, Leo G.; Wilson, Nicholas E. 9 2013 Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements. Zbl 1312.76025Cousins, Benjamin R.; Le Borne, Sabine; Linke, Alexander; Rebholz, Leo G.; Wang, Zhen 8 2013 The Leray-\(\alpha\beta\)-deconvolution model: energy analysis and numerical algorithms. Zbl 1351.76049Bowers, Abigail L.; Kim, Tae-Yeon; Neda, Monika; Rebholz, Leo G.; Fried, Eliot 5 2013 Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems. Zbl 1376.65034Le Borne, Sabine; Rebholz, Leo G. 5 2013 Well-posedness of a reduced order approximate deconvolution turbulence model. Zbl 1306.35099Rebholz, Leo G. 3 2013 On the enforcement of discrete mass conservation in incompressible flow simulations with continuous velocity approximation. Zbl 1287.76165D’Agnillo, Erica M.; Rebholz, Leo G. 1 2013 Approximate deconvolution models of turbulence. Analysis, phenomenology and numerical analysis. Zbl 1241.76002Layton, William J.; Rebholz, Leo 51 2012 Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection. Zbl 1253.76057Galvin, Keith J.; Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E. 38 2012 Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows. Zbl 1268.76014Kuberry, Paul; Larios, Adam; Rebholz, Leo G.; Wilson, Nicholas E. 17 2012 Modular nonlinear filter stabilization of methods for higher Reynolds numbers flow. Zbl 1294.76197Layton, William; Rebholz, Leo G.; Trenchea, Catalin 16 2012 Increasing accuracy and efficiency in FE computations of the Leray-deconvolution model. Zbl 1414.76035Bowers, Abigail L.; Rebholz, Leo G. 13 2012 A deconvolution enhancement of the Navier-Stokes-\({\alpha}{\beta}\) model. Zbl 1404.76140Kim, Tae-Yeon; Rebholz, Leo G.; Fried, Eliot 9 2012 Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering. Zbl 1412.76044Bowers, A. L.; Rebholz, L. G.; Takhirov, A.; Trenchea, C. 6 2012 Assessment of a vorticity based solver for the Navier-Stokes equations. Zbl 1352.76040Benzi, Michele; Olshanskii, Maxim A.; Rebholz, Leo G.; Wang, Zhen 5 2012 A mathematical and physical study of multiscale deconvolution models of turbulence. Zbl 1247.35089Dunca, Argus Adrian; Kohler, Kara E.; Neda, Monika; Rebholz, Leo G. 3 2012 A connection between Scott-Vogelius and grad-div stabilized Taylor-Hood FE approximations of the Navier-Stokes equations. Zbl 1244.76021Case, Michael A.; Ervin, Vincent J.; Linke, Alexander; Rebholz, Leo G. 58 2011 On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems. Zbl 1331.76038Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E. 25 2011 Enabling numerical accuracy of Navier-Stokes-\(\alpha\) through deconvolution and enhanced stability. Zbl 1267.76021Manica, Carolina C.; Neda, Monika; Olshanskii, Maxim; Rebholz, Leo G. 23 2011 On error analysis for the 3D Navier-Stokes equations in velocity-vorticity-helicity form. Zbl 1222.35143Lee, Hyesuk K.; Olshanskii, Maxim A.; Rebholz, Leo G. 14 2011 On an efficient finite element method for Navier-Stokes-\(\overline{\omega}\) with strong mass conservation. Zbl 1283.76018Manica, Carolina C.; Neda, Monika; Olshanskii, Maxim; Rebholz, Leo G.; Wilson, Nicholas E. 10 2011 A numerical study of the Navier-Stokes-\(\alpha \beta \) model. Zbl 1230.76027Kim, Tae-Yeon; Neda, Monika; Rebholz, Leo G.; Fried, Eliot 9 2011 Application of barycenter refined meshes in linear elasticity and incompressible fluid dynamics. Zbl 1426.74302Olshanskii, Maxim A.; Rebholz, Leo G. 8 2011 Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations. Zbl 1432.76077Cousins, Benjamin R.; Rebholz, Leo G.; Wilson, Nicholas E. 6 2011 Stable computing with an enhanced physics based scheme for the 3D Navier-Stokes equations. Zbl 1429.76069Case, Michael A.; Ervin, Vincent J.; Linke, Alexander; Rebholz, Leo G.; Wilson, Nicholas E. 3 2011 Small-scale divergence penalization for incompressible flow problems via time relaxation. Zbl 1381.76159Connors, Jeffrey M.; Jenkins, Eleanor W.; Rebholz, Leo G. 2 2011 Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations. Zbl 1406.76031Layton, William; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 29 2010 Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations. Zbl 1334.76083Olshanskii, Maxim A.; Rebholz, Leo G. 20 2010 On the high accuracy NS-alpha-deconvolution turbulence model. Zbl 1187.76720Rebholz, Leo G.; Sussman, Myron M. 10 2010 An enhanced-physics-based scheme for the NS-\(\alpha \) turbulence model. Zbl 1426.76191Miles, William W.; Rebholz, Leo G. 10 2010 Energy and helicity dissipation rates of the NS-alpha and NS-alpha-deconvolution models. Zbl 1423.76160Layton, William; Rebholz, Leo; Sussman, Myron 9 2010 Note on helicity balance of the Galerkin method for the 3D Navier-Stokes equations. Zbl 1227.76037Olshanskii, Maxim; Rebholz, Leo G. 6 2010 Temporally regularized direct numerical simulation. Zbl 1339.76037Layton, William J.; Pruett, C. David; Rebholz, Leo G. 4 2010 New connections between finite element formulations of the Navier-Stokes equations. Zbl 1427.76120Bowers, Abigail L.; Cousins, Benjamin R.; Linke, Alexander; Rebholz, Leo G. 3 2010 The stabilized extrapolated trapezoidal finite element method for the Navier-Stokes equations. Zbl 1229.76051Labovsky, Alexandr; Layton, William J.; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 39 2009 On the accuracy of the rotation form in simulations of the Navier-Stokes equations. Zbl 1161.76030Layton, William; Manica, Carolina C.; Neda, Monika; Olshanskii, Maxim; Rebholz, Leo G. 59 2008 Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence. Zbl 1191.76061Layton, William; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 54 2008 A family of new, high order NS-\(\alpha \) models arising from helicity correction in Leray turbulence models. Zbl 1138.35078Rebholz, Leo G. 17 2008 Helicity and energy conservation and dissipation in approximate deconvolution LES models of turbulence. Zbl 1176.76046Layton, William J.; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G. 9 2008 Conservation laws of turbulence models. Zbl 1110.76028Rebholz, Leo G. 26 2007 An energy- and helicity-conserving finite element scheme for the Navier-Stokes equations. Zbl 1141.76039Rebholz, Leo G. 16 2007 A multiscale V-P discretization for flow problems. Zbl 1091.76037Rebholz, Leo G. 1 2006 all cited Publications top 5 cited Publications all top 5 Cited by 639 Authors 80 Rebholz, Leo G. 28 Linke, Alexander 23 Layton, William J. 19 Neda, Monika 15 Olshanskii, Maxim A. 14 He, Yinnian 13 Kaya, Songul 13 Merdon, Christian 12 Dunca, Argus Adrian 12 Jiang, Nan 12 Neilan, Michael 11 Iliescu, Traian 11 Kim, Tae-Yeon 11 San, Omer 10 Huang, Pengzhan 9 Hou, Yanren 9 John, Volker 9 Manica, Carolina Cardoso 9 Schneier, Michael 9 Wilson, Nicholas E. 9 Xiao, Mengying 8 DeCaria, Victor P. 8 Larios, Adam 8 Lube, Gert 8 Mohebujjaman, Muhammad 8 Zhang, Shangyou 7 Akbas, Mine 7 Lederer, Philip Lukas 7 Maulik, Romit 7 Novo, Julia 7 Rhebergen, Sander 7 Trenchea, Catalin 6 Ahmed, Naveed 6 Berselli, Luigi Carlo 6 Çibik, Aytekin Bayram 6 Guzmán, Johnny 6 Heister, Timo 6 Jiang, Yaolin 6 Lehrenfeld, Christoph 6 Rozza, Gianluigi 6 Schroeder, Philipp W. 6 Singler, John R. 6 Wang, Zhu 6 Yang, Yunbo 5 Aggul, Mustafa 5 Beirão da Veiga, Lourenço 5 Bowers, Abigail L. 5 Fried, Eliot 5 García-Archilla, Bosco 5 He, Xiaoming 5 Labovsky, Alexander E. 5 Pollock, Sara 5 Quaini, Annalisa 5 Schöberl, Joachim 5 Vacca, Giuseppe 5 Wells, Garth N. 5 Zerfas, Camille 4 Arndt, Daniel 4 Barrenechea, Gabriel R. 4 Connors, Jeffrey Mark 4 Dassi, Franco 4 Eroglu, Fatma G. 4 Ervin, Vincent J. 4 Fiordilino, Joseph Anthony 4 Jenkins, Eleanor W. 4 Mora, David 4 Mu, Lin 4 Rubino, Samuele 4 Scott, Larkin Ridgway 4 Shang, Yueqiang 4 Waters, Jiajia Wang 4 Wechsung, Florian 4 Ye, Xiu 4 Zhang, Guodong 4 Zhang, Shuo 3 Breckling, Sean 3 Cousins, Benjamin R. 3 Dallmann, Helene 3 de Frutos, Javier 3 Demir, Medine 3 Erkmen, Dilek 3 Farrell, Patrick Emmet 3 Feng, Minfu 3 Fu, Guosheng 3 Galvin, Keith J. 3 Gerritsma, Marc I. 3 Girfoglio, Michele 3 Gunzburger, Max D. 3 Jiang, Wen 3 Kean, Kiera 3 Koc, Birgul 3 Le Borne, Sabine 3 Lewandowski, Roger 3 Li, Lingxiao 3 Mou, Changhong 3 Oyarzúa, Ricardo 3 Pahlevani, Fran 3 Palha, Artur 3 Pei, Yuan 3 Rong, Yao ...and 539 more Authors all top 5 Cited in 85 Serials 56 Computer Methods in Applied Mechanics and Engineering 38 Journal of Computational Physics 29 SIAM Journal on Numerical Analysis 29 Journal of Scientific Computing 26 Computers & Mathematics with Applications 23 Journal of Computational and Applied Mathematics 22 SIAM Journal on Scientific Computing 19 Journal of Mathematical Analysis and Applications 18 Applied Mathematics and Computation 16 Computers and Fluids 16 Numerical Methods for Partial Differential Equations 11 Applied Numerical Mathematics 11 Advances in Computational Mathematics 10 International Journal of Computer Mathematics 10 Computational Methods in Applied Mathematics 9 Mathematics of Computation 9 Calcolo 8 Discrete and Continuous Dynamical Systems. 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(English Edition) 1 AIMS Mathematics all top 5 Cited in 27 Fields 417 Fluid mechanics (76-XX) 364 Numerical analysis (65-XX) 185 Partial differential equations (35-XX) 19 Biology and other natural sciences (92-XX) 14 Mechanics of deformable solids (74-XX) 11 Geophysics (86-XX) 11 Systems theory; control (93-XX) 9 Ordinary differential equations (34-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Computer science (68-XX) 4 Optics, electromagnetic theory (78-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistics (62-XX) 2 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Mathematics education (97-XX) Citations by Year