Edit Profile Carstensen, Carsten Compute Distance To: Compute Author ID: carstensen.carsten Published as: Carstensen, C.; Carstensen, Carsten Homepage: http://www2.mathematik.hu-berlin.de/~cc/cc_homepage/cc/education.shtml External Links: MGP · ResearchGate · dblp · GND Documents Indexed: 281 Publications since 1987, including 3 Books all top 5 Co-Authors 42 single-authored 16 Funken, Stefan A. 13 Gallistl, Dietmar 12 Bartels, Sören 12 Gedicke, Joscha 11 Praetorius, Dirk 11 Stephan, Ernst Peter 9 Hoppe, Ronald H. W. 9 Merdon, Christian 9 Wriggers, Peter 8 Alberty, Jochen 8 Schedensack, Mira 7 Nataraj, Neela 7 Orlando, Antonio 7 Petković, Miodrag S. 7 Rabus, Hella 6 Bringmann, Philipp 6 Dolzmann, Georg 6 Hackl, Klaus 6 Klose, Roland 6 Peterseim, Daniel 6 Plecháč, Petr 5 Hellwig, Friederike 5 Park, Eun-Jae 5 Weinberg, Kerstin 5 Zarrabi, Darius 4 Braess, Dietrich 4 Demkowicz, Leszek F. 4 Hu, Jun 4 Stein, Erwin 3 Beckermann, Bernhard 3 Dond, Asha K. 3 Eigel, Martin 3 Gopalakrishnan, Jay 3 Hoppe, Ulrich 3 Köhler, Karoline 3 Pani, Amiya Kumar 3 Prohl, Andreas 3 Reddy, B. Dayanand 3 Scherf, Oliver 3 Valdman, Jan 2 Allix, Olivier 2 Boiger, Wolfgang 2 Bösing, Paulo Rafael 2 Brenner, Susanne Cecelia 2 Brokate, Martin 2 Conti, Sergio 2 Engquist, Bjorn E. 2 Günther, David 2 Gwinner, Joachim 2 Hecht, Axel 2 Hu, Jun 2 Jansche, Stefan 2 Jensen, Max 2 Liu, Dongjie 2 Liu, Steve Wenbin 2 Maischak, Matthias 2 Mallik, Gouranga 2 Mehrmann, Volker 2 Międlar, Agnieszka 2 Monk, Peter B. 2 Mühlbach, Günter W. 2 Puttkammer, Sophie 2 Schroder, Andreas 2 Schröder, Jörg 2 Thiele, Jan 2 Xie, Xiaoping 2 Yan, Ningning 2 Yu, Guozhu 1 Ainsworth, Mark 1 Altmann, Robert 1 Bahriawati, C. 1 Brink, Ulrich 1 Buffa, Annalisa 1 Carstensen, Christine 1 Causin, Paola 1 Dörfler, Willy 1 Ebobisse, François Bille 1 Estep, Donald J. 1 Faermann, Birgit 1 Feischl, Michael 1 Gerritsma, Marc I. 1 Gudi, Thirupathi 1 Hackbusch, Wolfgang 1 Helm, D. S. 1 Hu, Jun 1 Huang, Yunqing 1 Huth, Robert 1 Jochimsen, K. 1 Kim, Dongho 1 Krämer, Boris 1 Kuhn, Michael A. 1 Langer, Ulrich 1 Lazarov, Raytcho D. 1 Li, Zhiping 1 Löbhard, Caroline 1 McBride, Andrew T. 1 Mielke, Alexander 1 Müller, Stefan 1 Neumann, Johannes 1 Ohnimus, Stephan ...and 31 more Co-Authors all top 5 Serials 46 Numerische Mathematik 36 SIAM Journal on Numerical Analysis 18 Computer Methods in Applied Mechanics and Engineering 18 Mathematics of Computation 10 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 9 Computers & Mathematics with Applications 9 IMA Journal of Numerical Analysis 9 Oberwolfach Reports 7 SIAM Journal on Scientific Computing 7 Computational Methods in Applied Mathematics 6 Computing 6 Journal of Computational and Applied Mathematics 6 Journal of Computational Mathematics 6 PAMM. Proceedings in Applied Mathematics and Mechanics 5 International Journal for Numerical Methods in Engineering 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Applied Numerical Mathematics 4 Journal of Numerical Mathematics 3 Mathematical Methods in the Applied Sciences 3 Computational Mechanics 3 Numerical Methods for Partial Differential Equations 3 Numerical Algorithms 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 BIT 2 Constructive Approximation 2 SIAM Journal on Mathematical Analysis 2 Numerical Mathematics: Theory, Methods and Applications 1 Applicable Analysis 1 Journal of the Australian Mathematical Society, Series B 1 Mathematische Semesterberichte 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Approximation Theory 1 Mathematische Nachrichten 1 Quarterly of Applied Mathematics 1 Computer Aided Geometric Design 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Facta Universitatis. Series Mathematics and Informatics 1 Journal of Scientific Computing 1 Journal of Integral Equations and Applications 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 Serdica 1 Studia Universitatis Babeş-Bolyai. Mathematica 1 Continuum Mechanics and Thermodynamics 1 Communications in Numerical Methods in Engineering 1 Numerical Linear Algebra with Applications 1 East-West Journal of Numerical Mathematics 1 Advances in Computational Mathematics 1 Engineering Analysis with Boundary Elements 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 International Journal of Numerical Analysis and Modeling 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 GAMM-Mitteilungen 1 CISM International Centre for Mechanical Sciences. Courses and Lectures 1 Lecture Notes in Computational Science and Engineering all top 5 Fields 231 Numerical analysis (65-XX) 108 Mechanics of deformable solids (74-XX) 97 Partial differential equations (35-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 18 Fluid mechanics (76-XX) 15 Functions of a complex variable (30-XX) 13 General and overarching topics; collections (00-XX) 12 Field theory and polynomials (12-XX) 10 Optics, electromagnetic theory (78-XX) 9 Real functions (26-XX) 6 Approximations and expansions (41-XX) 6 Integral equations (45-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Mechanics of particles and systems (70-XX) 1 Number theory (11-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 241 Publications have been cited 3,225 times in 1,562 Documents Cited by ▼ Year ▼ A posteriori error estimate for the mixed finite element method. Zbl 0864.65068Carstensen, Carsten 120 1997 Non-convex potentials and microstructures in finite-strain plasticity. Zbl 1008.74016Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander 113 2002 Edge residuals dominate a posteriori error estimates for low order finite element methods. Zbl 0938.65124Carstensen, Carsten; Verfürth, Rüdiger 72 1999 Axioms of adaptivity. Zbl 1350.65119Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 71 2014 Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I: Low order conforming, nonconforming, and mixed FEM. Zbl 0997.65126Carstensen, Carsten; Bartels, Sören 70 2002 Quasi-interpolation and a posteriori error analysis in finite element methods. Zbl 0948.65113Carstensen, Carsten 57 1999 Remarks around 50 lines of Matlab: short finite element implementation. Zbl 0938.65129Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A. 57 1999 A posteriori error estimates for mixed FEM in elasticity. Zbl 0928.74093Carstensen, Carsten; Dolzmann, Georg 48 1998 An a posteriori error estimate for a first-kind integral equation. Zbl 0854.65102Carstensen, Carsten 48 1997 A unifying theory of a posteriori error control for nonconforming finite element methods. Zbl 1127.65083Carstensen, C.; Hu, Jun 46 2007 A posteriori error estimates for nonconforming finite element methods. Zbl 1010.65044Carstensen, Carsten; Bartels, Sören; Jansche, Stefan 45 2002 Breaking spaces and forms for the DPG method and applications including Maxwell equations. Zbl 1359.65249Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. 43 2016 A unifying theory of a posteriori finite element error control. Zbl 1100.65089Carstensen, C. 42 2005 Error reduction and convergence for an adaptive mixed finite element method. Zbl 1094.65112Carstensen, Carsten; Hoppe, R. H. W. 41 2006 Three Matlab implementations of the lowest-order Raviart-Thomas MFEM with a posteriori error control. Zbl 1086.65107Bahriawati, C.; Carstensen, C. 41 2005 Framework for the a posteriori error analysis of nonconforming finite elements. Zbl 1165.65072Carstensen, Carsten; Hu, Jun; Orlando, Antonio 38 2007 Averaging techniques yield reliable a posteriori finite element error control for obstacle problems. Zbl 1063.65050Bartels, S.; Carstensen, C. 38 2004 Numerical solution of the scalar double-well problem allowing microstructure. Zbl 0870.65055Carstensen, Carsten; Plechác, Petr 36 1997 A posteriori error estimate and h-adaptive algorithm on surfaces from Symm’s integral equation. Zbl 1018.65138Carstensen, C.; Maischak, M.; Stephan, E. P. 35 2001 A posteriori error estimates for boundary element methods. Zbl 0831.65120Carstensen, Carsten; Stephan, Ernst P. 35 1995 Convergence analysis of an adaptive nonconforming finite element method. Zbl 1101.65102Carstensen, Carsten; Hoppe, Ronald H. W. 34 2006 Weierstrass formula and zero-finding methods. Zbl 0821.65028Petković, Miodrag S.; Carstensen, Carsten; Trajkovíc, Miroslav 34 1995 Convergence analysis of a conforming adaptive finite element method for an obstacle problem. Zbl 1126.65058Braess, Dietrich; Carstensen, Carsten; Hoppe, Ronald H. W. 33 2007 Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods. Zbl 0973.65091Carstensen, C.; Funken, S. A. 33 2000 Effective relaxation for microstructure simulations: algorithms and applications. Zbl 1112.74501Bartels, S.; Carstensen, C.; Hackl, K.; Hoppe, U. 32 2004 Guaranteed lower bounds for eigenvalues. Zbl 1320.65162Carstensen, Carsten; Gedicke, Joscha 31 2014 Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. Zbl 1062.65113Bartels, S.; Carstensen, C.; Dolzmann, G. 31 2004 Fully reliable localized error control in the FEM. Zbl 0956.65099Carstensen, Carsten; Funken, Stefan A. 31 2000 Matlab implementation of the finite element method in elasticity. Zbl 1239.74092Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A.; Klose, Roland 30 2002 A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems. Zbl 1014.76042Carstensen, Carsten; Funken, Stefan A. 29 2001 Averaging technique for FE – a posteriori error control in elasticity. I: Conforming FEM. Zbl 0981.74063Carstensen, Carsten; Funken, Stefan A. 29 2001 Guaranteed lower eigenvalue bounds for the biharmonic equation. Zbl 1298.65165Carstensen, Carsten; Gallistl, Dietmar 27 2014 Residual-based a posteriori error estimate for hypersingular equation on surfaces. Zbl 1063.65116Carstensen, Carsten; Maischak, M.; Praetorius, D.; Stephan, E. P. 27 2004 Adaptive numerical analysis in primal elastoplasticity with hardening. Zbl 0956.74049Alberty, Jochen; Carstensen, Carsten; Zarrabi, Darius 27 1999 A posteriori error control for DPG methods. Zbl 1320.65171Carstensen, Carsten; Demkowicz, Leszek; Gopalakrishnan, Jay 26 2014 An oscillation-free adaptive FEM for symmetric eigenvalue problems. Zbl 1227.65106Carstensen, Carsten; Gedicke, Joscha 26 2011 Explicit and averaging a posteriori error estimates for adaptive finite volume methods. Zbl 1084.65112Carstensen, C.; Lazarov, R.; Tomov, S. 26 2005 Adaptive coupling of boundary elements and finite elements. Zbl 0849.65083Carstensen, Carsten; Stephan, Ernst P. 25 1995 Uniform convergence and a posteriori error estimators for the enhanced strain finite element method. Zbl 1050.65097Braess, D.; Carstensen, C.; Reddy, B. D. 24 2004 Local stress regularity in scalar nonconvex variational problems. Zbl 1012.49027Carstensen, Carsten; Müller, Stefan 24 2002 Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for \(H^1\)-stability of the \(L^2\)-projection onto finite element spaces. Zbl 0989.65123Carstensen, Carsten 24 2002 Some improved inclusion methods for polynomial roots with Weierstrass’ corrections. Zbl 0776.65036Petković, Miodrag S.; Carstensen, Carsten 24 1993 Adaptive boundary element methods for some first kind integral equations. Zbl 0863.65073Carstensen, Carsten; Stephan, Ernst P. 23 1996 A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the Stokes problem. Zbl 1232.65098Carstensen, Carsten; Kim, Dongho; Park, Eun-Jae 22 2011 Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124Carstensen, Carsten; Praetorius, Dirk 22 2006 A review of unified a posteriori finite element error control. Zbl 1289.65249Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 21 2012 On the adaptive coupling of FEM and BEM in 2-d elasticity. Zbl 0880.73062Carstensen, C.; Funken, S. A.; Stephan, E. P. 21 1997 Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods. Zbl 1274.65290Carstensen, Carsten; Gedicke, Joscha; Rim, Donsub 20 2012 All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable. Zbl 1067.65115Carstensen, C. 20 2004 Numerical approximation of Young measures in non-convex variational problems. Zbl 0945.65070Carstensen, Carsten; Roubíček, Tomáš 20 2000 Efficiency of a posteriori BEM-error estimates for first-kind integral equations on quasi-uniform meshes. Zbl 0849.65084Carstensen, Carsten 20 1996 Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis. Zbl 1073.65120Carstensen, Carsten 19 2004 Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. II: Higher order FEM. Zbl 0997.65127Bartels, Sören; Carstensen, Carsten 19 2002 An adaptive mesh-refining algorithm allowing for an \(H^1\) stable \(L^2\) projection onto Courant finite element spaces. Zbl 1064.65143Carstensen, Carsten 18 2004 A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems. Zbl 0954.65052Carstensen, Carsten; Gwinner, Joachim 18 1999 Numerical analysis of the primal problem of elastoplasticity with hardening. Zbl 0947.74061Carstensen, Carsten 18 1999 Adaptive finite elements for elastic bodies in contact. Zbl 0940.74058Carstensen, C.; Scherf, O.; Wriggers, P. 18 1999 Comparison results of finite element methods for the Poisson model problem. Zbl 1261.65115Carstensen, C.; Peterseim, D.; Schedensack, M. 17 2012 The arnold-winther mixed FEM in linear elasticity. I: Implementation and numerical verification. Zbl 1194.74374Carstensen, C.; Günther, D.; Reininghaus, J.; Thiele, J. 17 2008 Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089Carstensen, Carsten; Praetorius, Dirk 17 2007 On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials. Zbl 0779.65030Carstensen, Carsten 17 1993 An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity. Zbl 1254.65123Carstensen, Carsten; Gedicke, Joscha 16 2012 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172Carstensen, C.; Eigel, M.; Gedicke, J. 16 2011 An optimal adaptive mixed finite element method. Zbl 1215.65173Carstensen, Carsten; Rabus, Hella 16 2011 A unifying theory of a posteriori error control for discontinuous Galerkin FEM. Zbl 1169.65106Carstensen, Carsten; Gudi, Thirupathi; Jensen, Max 16 2009 Locking-free adaptive mixed finite element methods in linear elasticity. Zbl 1004.74068Carstensen, C.; Dolzmann, G.; Funken, S. A.; Helm, D. S. 16 2000 Fast parallel solvers for symmetric boundary element domain decomposition equations. Zbl 0907.65119Carstensen, C.; Kuhn, M.; Langer, U. 16 1998 Interface problem in holonomic elastoplasticity. Zbl 0792.73017Carstensen, Carsten 16 1993 Convergence and optimality of adaptive least squares finite element methods. Zbl 1327.65212Carstensen, Carsten; Park, Eun-Jae 15 2015 Optimal adaptive nonconforming FEM for the Stokes problem. Zbl 1316.76046Carstensen, Carsten; Peterseim, Daniel; Rabus, Hella 15 2013 Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations. Zbl 1073.78008Carstensen, C.; Hoppe, R. H. W. 15 2005 Elastoviscoplastic finite element analysis in 100 lines of Matlab. Zbl 1099.74544Carstensen, C.; Klose, R. 15 2002 Mathematical foundation of a posteriori error estimates and adaptive mesh-refining algorithms for boundary integral equations of the first kind. Zbl 1007.65100Carstensen, C.; Faermann, B. 15 2001 Numerical analysis of compatible phase transitions in elastic solids. Zbl 1049.74062Carstensen, Carsten; Plechác, Petr 15 2000 Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. Zbl 06662514Carstensen, C.; Hellwig, F. 14 2016 Quasi-optimal adaptive pseudostress approximation of the Stokes equations. Zbl 1383.76333Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 14 2013 Estimator competition for Poisson problems. Zbl 1224.65253Carstensen, C.; Merdon, C. 14 2010 Hanging nodes in the unifying theory of a posteriori finite element error control. Zbl 1212.65423Carstensen, C.; Hu, Jun 14 2009 Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. Zbl 1007.74062Carstensen, Carsten; Plecháč, Petr 14 2001 Axioms of adaptivity with separate marking for data resolution. Zbl 1377.65147Carstensen, C.; Rabus, H. 13 2017 A posteriori error estimators for convection-diffusion eigenvalue problems. Zbl 1295.65108Gedicke, J.; Carstensen, C. 13 2014 Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. Zbl 1285.65079Carstensen, C.; Merdon, C. 13 2013 A posteriori finite element error control for the \(p\)-Laplace problem. Zbl 1050.65101Carstensen, Carsten; Klose, R. 13 2003 Adaptive finite element methods for microstructures? Numerical experiments for a 2-well benchmark. Zbl 1090.74054Carstensen, C.; Jochimsen, K. 13 2003 FEM and BEM coupling for a nonlinear transmission problem with Signorini contact. Zbl 0896.65079Carstensen, Carsten; Gwinner, Joachim 13 1997 Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics. Zbl 0877.73063Brink, Ulrich; Carstensen, Carsten; Stein, Erwin 13 1996 Adaptive finite element analysis of geometrically nonlinear plates and shells, especially buckling. Zbl 0809.73072Stein, Erwin; Seifert, B.; Ohnimus, S.; Carstensen, Carsten 13 1994 On iteration methods without derivatives for the simultaneous determination of polynomial zeros. Zbl 0776.65033Carstensen, Carsten; Petković, Miodrag S. 13 1993 A posteriori error estimate for the symmetric coupling of finite elements and boundary elements. Zbl 0863.65070Carstensen, C. 12 1996 Inclusion of the roots of a polynomial based on Gerschgorin’s theorem. Zbl 0726.65053Carstensen, C. 12 1991 Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Zbl 1311.65136Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 11 2015 Low-order dPG-FEM for an elliptic PDE. Zbl 1364.65242Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L. 11 2014 A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates. Zbl 1225.74081Carstensen, Carsten; Xie, Xiaoping; Yu, Guozhu; Zhou, Tianxiao 11 2011 Averaging techniques for reliable a posteriori FE error control in elastoplasticity with hardening. Zbl 1026.74067Carstensen, Carsten; Alberty, Jochen 11 2003 Residual-based a posteriori error estimate for a nonconforming Reissner–Mindlin plate finite element. Zbl 1042.74049Carstensen, Carsten 11 2002 Domain decomposition for a non-smooth convex minimization problem and its application to plasticity. Zbl 0890.49015Carstensen, C. 11 1997 Linear construction of companion matrices. Zbl 0717.15011Carstensen, C. 11 1991 Comparison results and unified analysis for first-order finite volume element methods for a Poisson model problem. Zbl 1433.65254Carstensen, Carsten; Nataraj, Neela; Pani, Amiya K. 10 2016 Medius analysis and comparison results for first-order finite element methods in linear elasticity. Zbl 1329.74272Carstensen, C.; Schedensack, M. 10 2015 An adaptive homotopy approach for non-selfadjoint eigenvalue problems. Zbl 1263.65106Carstensen, Carsten; Gedicke, Joscha; Mehrmann, Volker; Miedlar, Agnieszka 10 2011 Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity. Zbl 07315149Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 1 2021 How to prove the discrete reliability for nonconforming finite element methods. Zbl 07295184Carstensen, Carsten; Puttkammer, Sophie 1 2020 Collective marking for adaptive least-squares finite element methods with optimal rates. Zbl 1426.65171Carstensen, Carsten 1 2020 A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations. Zbl 07208101Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 1 2019 Quasi-optimality of adaptive mixed FEMs for non-selfadjoint indefinite second-order linear elliptic problems. Zbl 1420.65108Carstensen, Carsten; Dond, Asha K.; Rabus, Hella 1 2019 Nonlinear discontinuous Petrov-Galerkin methods. Zbl 1398.65292Carstensen, C.; Bringmann, P.; Hellwig, F.; Wriggers, P. 7 2018 An adaptive least-squares FEM for linear elasticity with optimal convergence rates. Zbl 06838253Bringmann, P.; Carstensen, C.; Starke, Gerhard 5 2018 Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation. Zbl 1401.65130Carstensen, Carsten; Hellwig, Friederike 4 2018 A low-order discontinuous Petrov-Galerkin method for the Stokes equations. Zbl 1401.65131Carstensen, Carsten; Puttkammer, Sophie 4 2018 Asymptotic exactness of the least-squares finite element residual. Zbl 1397.65230Carstensen, Carsten; Storn, Johannes 4 2018 Optimal convergence rates for adaptive lowest-order discontinuous Petrov-Galerkin schemes. Zbl 1395.65140Carstensen, Carsten; Hellwig, Friederike 2 2018 Three first-order finite volume element methods for Stokes equations under minimal regularity assumptions. Zbl 1412.65181Carstensen, Carsten; Dond, Asha K.; Nataraj, Neela; Pani, Amiya K. 1 2018 Axioms of adaptivity with separate marking for data resolution. Zbl 1377.65147Carstensen, C.; Rabus, H. 13 2017 Nonconforming FEM for the obstacle problem. Zbl 1433.65284Carstensen, C.; Köhler, K. 6 2017 Convergence of natural adaptive least squares finite element methods. Zbl 1378.65176Carstensen, Carsten; Park, Eun-Jae; Bringmann, Philipp 6 2017 An adaptive least-squares FEM for the Stokes equations with optimal convergence rates. Zbl 1381.76156Bringmann, P.; Carstensen, C. 5 2017 \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates. Zbl 1402.65150Bringmann, P.; Carstensen, C. 1 2017 Flow relations and yield functions for dissipative strain-gradient plasticity. Zbl 1382.74023Carstensen, Carsten; Ebobisse, François; McBride, Andrew T.; Reddy, B. Daya; Steinmann, Paul 1 2017 Efficient discrete Lagrange multipliers in three first-order finite element discretizations for the a posteriori error control in an obstacle problem. Zbl 1359.65101Carstensen, C.; Köhler, K. 1 2017 Breaking spaces and forms for the DPG method and applications including Maxwell equations. Zbl 1359.65249Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. 43 2016 Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. Zbl 06662514Carstensen, C.; Hellwig, F. 14 2016 Comparison results and unified analysis for first-order finite volume element methods for a Poisson model problem. Zbl 1433.65254Carstensen, Carsten; Nataraj, Neela; Pani, Amiya K. 10 2016 \(L^{2}\) best approximation of the elastic stress in the Arnold-Winther FEM. Zbl 1433.74102Carstensen, C.; Gallistl, D.; Schedensack, M. 5 2016 Error analysis of nonconforming and mixed FEMs for second-order linear non-selfadjoint and indefinite elliptic problems. Zbl 1342.65214Carstensen, Carsten; Dond, Asha K.; Nataraj, Neela; Pani, Amiya K. 5 2016 Guaranteed velocity error control for the pseudostress approximation of the Stokes equations. Zbl 1401.76083Bringmann, P.; Carstensen, C.; Merdon, C. 4 2016 The norm of a discretized gradient in \(H(\mathrm{div})^*\) for a posteriori finite element error analysis. Zbl 1352.65440Carstensen, Carsten; Peterseim, Daniel; Schröder, Andreas 4 2016 Justification of the saturation assumption. Zbl 1348.65161Carstensen, C.; Gallistl, D.; Gedicke, J. 3 2016 A natural nonconforming FEM for the Bingham flow problem is quasi-optimal. Zbl 06566213Carstensen, C.; Reddy, B. D.; Schedensack, M. 2 2016 Robust residual-based a posteriori Arnold-winther mixed finite element analysis in elasticity. Zbl 1425.74455Carstensen, Carsten; Gedicke, Joscha 1 2016 Convergence and optimality of adaptive least squares finite element methods. Zbl 1327.65212Carstensen, Carsten; Park, Eun-Jae 15 2015 Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Zbl 1311.65136Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 11 2015 Medius analysis and comparison results for first-order finite element methods in linear elasticity. Zbl 1329.74272Carstensen, C.; Schedensack, M. 10 2015 Comparison results for the Stokes equations. Zbl 1320.76062Carstensen, C.; Köhler, K.; Peterseim, D.; Schedensack, M. 5 2015 An optimal adaptive finite element method for an obstacle problem. Zbl 1317.65232Carstensen, Carsten; Hu, Jun 4 2015 Comparison results of nonstandard \(P_2\) finite element methods for the biharmonic problem. Zbl 1327.65211Carstensen, Carsten; Gallistl, Dietmar; Nataraj, Neela 3 2015 Nonconforming FEMs for an optimal design problem. Zbl 1312.74036Carstensen, C.; Liu, D. J. 3 2015 Discontinuous Galerkin with weakly over-penalized techniques for Reissner-Mindlin plates. Zbl 1329.74269Bösing, Paulo Rafael; Carstensen, Carsten 1 2015 Weakly over-penalized discontinuous Galerkin schemes for Reissner-Mindlin plates without the shear variable. Zbl 1401.65128Bösing, Paulo Rafael; Carstensen, Carsten 1 2015 Axioms of adaptivity. Zbl 1350.65119Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 71 2014 Guaranteed lower bounds for eigenvalues. Zbl 1320.65162Carstensen, Carsten; Gedicke, Joscha 31 2014 Guaranteed lower eigenvalue bounds for the biharmonic equation. Zbl 1298.65165Carstensen, Carsten; Gallistl, Dietmar 27 2014 A posteriori error control for DPG methods. Zbl 1320.65171Carstensen, Carsten; Demkowicz, Leszek; Gopalakrishnan, Jay 26 2014 A posteriori error estimators for convection-diffusion eigenvalue problems. Zbl 1295.65108Gedicke, J.; Carstensen, C. 13 2014 Low-order dPG-FEM for an elliptic PDE. Zbl 1364.65242Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L. 11 2014 A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes. Zbl 1362.65123Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun 7 2014 Computational survey on a posteriori error estimators for the Crouzeix-Raviart nonconforming finite element method for the Stokes problem. Zbl 1285.65072Carstensen, Carsten; Merdon, Christian 7 2014 An adaptive finite element method with asymptotic saturation for eigenvalue problems. Zbl 1306.65272Carstensen, C.; Gedicke, J.; Mehrmann, V.; Miȩdlar, A. 2 2014 Refined fully explicit a posteriori residual-based error control. Zbl 1309.65124Carstensen, C.; Merdon, C. 1 2014 Optimal adaptive nonconforming FEM for the Stokes problem. Zbl 1316.76046Carstensen, Carsten; Peterseim, Daniel; Rabus, Hella 15 2013 Quasi-optimal adaptive pseudostress approximation of the Stokes equations. Zbl 1383.76333Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 14 2013 Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. Zbl 1285.65079Carstensen, C.; Merdon, C. 13 2013 Effective postprocessing for equilibration a posteriori error estimators. Zbl 1267.65162Carstensen, C.; Merdon, C. 7 2013 Discrete reliability for Crouzeix-Raviart FEMs. Zbl 1321.65171Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 6 2013 A posteriori error estimator competition for conforming obstacle problems. Zbl 1364.65243Carstensen, C.; Merdon, C. 5 2013 A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles. Zbl 1316.74060Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun 4 2013 Finite element network approximation of conductivity in particle composites. Zbl 1329.74284Peterseim, Daniel; Carstensen, Carsten 3 2013 Aspects of guaranteed error control in CPDEs. Zbl 1275.65075Carstensen, C.; Merdon, C.; Neumann, Johannes 1 2013 A review of unified a posteriori finite element error control. Zbl 1289.65249Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 21 2012 Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods. Zbl 1274.65290Carstensen, Carsten; Gedicke, Joscha; Rim, Donsub 20 2012 Comparison results of finite element methods for the Poisson model problem. Zbl 1261.65115Carstensen, C.; Peterseim, D.; Schedensack, M. 17 2012 An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity. Zbl 1254.65123Carstensen, Carsten; Gedicke, Joscha 16 2012 The adaptive nonconforming FEM for the pure displacement problem in linear elasticity is optimal and robust. Zbl 1397.74183Carstensen, Carsten; Rabus, Hella 7 2012 P\(_1\)-nonconforming finite elements on triangulations into triangles and quadrilaterals. Zbl 1251.65156Altmann, Robert; Carstensen, Carsten 7 2012 Convergence of adaptive boundary element methods. Zbl 1238.65124Carstensen, Carsten; Praetorius, Dirk 7 2012 Mixed finite element method for a degenerate convex variational problem from topology optimization. Zbl 1314.65088Carstensen, Carsten; Günther, David; Rabus, Hella 3 2012 Numerical experiments for the Arnold-Einther mixed finite elements for the Stokes problem. Zbl 1250.76130Carstensen, Carsten; Gedicke, Joscha; Park, Eun-Jae 2 2012 Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy. Zbl 1247.78051Carstensen, C.; Praetorius, D. 2 2012 An oscillation-free adaptive FEM for symmetric eigenvalue problems. Zbl 1227.65106Carstensen, Carsten; Gedicke, Joscha 26 2011 A priori and a posteriori pseudostress-velocity mixed finite element error analysis for the Stokes problem. Zbl 1232.65098Carstensen, Carsten; Kim, Dongho; Park, Eun-Jae 22 2011 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172Carstensen, C.; Eigel, M.; Gedicke, J. 16 2011 An optimal adaptive mixed finite element method. Zbl 1215.65173Carstensen, Carsten; Rabus, Hella 16 2011 A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates. Zbl 1225.74081Carstensen, Carsten; Xie, Xiaoping; Yu, Guozhu; Zhou, Tianxiao 11 2011 An adaptive homotopy approach for non-selfadjoint eigenvalue problems. Zbl 1263.65106Carstensen, Carsten; Gedicke, Joscha; Mehrmann, Volker; Miedlar, Agnieszka 10 2011 Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods. Zbl 1230.74205Yu, Guozhu; Xie, Xiaoping; Carstensen, Carsten 6 2011 An adaptive hybridized interior penalty discontinuous Galerkin method for H(curl)-elliptic problems. Zbl 1249.65228Carstensen, C.; Hoppe, R. H. W.; Sharma, N.; Warburton, T. 3 2011 Remarks on the state of the art of a posteriori error control of elliptic PDEs in energy norms in practise. Zbl 1265.65225Carstensen, Carsten; Merdon, Christian 1 2011 Estimator competition for Poisson problems. Zbl 1224.65253Carstensen, C.; Merdon, C. 14 2010 On the strong convergence of gradients in stabilized degenerate convex minimization problems. Zbl 1205.35062Boiger, Wolfgang; Carstensen, Carsten 3 2010 Analysis of a class of penalty methods for computing singular minimizers. Zbl 1283.65097Carstensen, C.; Ortner, C. 2 2010 A unifying theory of a posteriori error control for discontinuous Galerkin FEM. Zbl 1169.65106Carstensen, Carsten; Gudi, Thirupathi; Jensen, Max 16 2009 Hanging nodes in the unifying theory of a posteriori finite element error control. Zbl 1212.65423Carstensen, C.; Hu, Jun 14 2009 Error reduction in adaptive finite element approximations of elliptic obstacle problems. Zbl 1212.65246Braess, Dietrich; Carstensen, Carsten; Hoppe, Ronald H. W. 8 2009 Convergence of adaptive finite element methods in computational mechanics. Zbl 1419.74232Carstensen, Carsten 7 2009 Unified framework for an a posteriori error analysis of non-standard finite element approximations of H(curl)-elliptic problems. Zbl 1196.65171Carstensen, C.; Hoppe, R. H. W. 4 2009 Mixed finite element technologies. Zbl 1169.65002Wriggers, Peter (ed.); Carstensen, Carsten (ed.) 3 2009 Lectures on adaptive mixed finite element methods. Zbl 1181.65136Carstensen, C. 1 2009 The arnold-winther mixed FEM in linear elasticity. I: Implementation and numerical verification. Zbl 1194.74374Carstensen, C.; Günther, D.; Reininghaus, J.; Thiele, J. 17 2008 Mixed analytical-numerical relaxation in finite single-slip crystal plasticity. Zbl 1160.74326Carstensen, Carsten; Conti, Sergio; Orlando, Antonio 10 2008 Convergence of an adaptive FEM for a class of degenerate convex minimization problems. Zbl 1169.65065Carstensen, Carsten 6 2008 A posteriori error analysis for conforming MITC elements for Reissner-Mindlin plates. Zbl 1130.74045Carstensen, C.; Hu, Jun 5 2008 A convergent adaptive finite element method for an optimal design problem. Zbl 1144.74038Bartels, Sören; Carstensen, Carsten 4 2008 Partition of unity for localization in implicit a posteriori finite element error control for linear elasticity. Zbl 1195.74166Carstensen, Carsten; Thiele, Jan 3 2008 A unifying theory of a posteriori error control for nonconforming finite element methods. Zbl 1127.65083Carstensen, C.; Hu, Jun 46 2007 Framework for the a posteriori error analysis of nonconforming finite elements. Zbl 1165.65072Carstensen, Carsten; Hu, Jun; Orlando, Antonio 38 2007 Convergence analysis of a conforming adaptive finite element method for an obstacle problem. Zbl 1126.65058Braess, Dietrich; Carstensen, Carsten; Hoppe, Ronald H. W. 33 2007 Averaging techniques for the a posteriori BEM error control for a hypersingular integral equation in two dimensions. Zbl 1140.65089Carstensen, Carsten; Praetorius, Dirk 17 2007 Averaging techniques for a posteriori error control in finite element and boundary element analysis. Zbl 1298.65161Carstensen, Carsten; Praetorius, Dirk 9 2007 Error reduction and convergence for an adaptive mixed finite element method. Zbl 1094.65112Carstensen, Carsten; Hoppe, R. H. W. 41 2006 Convergence analysis of an adaptive nonconforming finite element method. Zbl 1101.65102Carstensen, Carsten; Hoppe, Ronald H. W. 34 2006 Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124Carstensen, Carsten; Praetorius, Dirk 22 2006 ...and 141 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,723 Authors 123 Carstensen, Carsten 53 Praetorius, Dirk 44 Petković, Miodrag S. 39 Gatica, Gabriel N. 36 Stephan, Ernst Peter 23 Führer, Thomas 21 Mosler, Jörn 20 Demkowicz, Leszek F. 20 Hu, Jun 20 Vohralík, Martin 19 Feischl, Michael 17 Karkulik, Michael 17 Park, Eun-Jae 16 Bartels, Sören 16 Gudi, Thirupathi 16 Mielke, Alexander 16 Valdman, Jan 15 Ern, Alexandre 15 Gedicke, Joscha 15 Heuer, Norbert 15 Wohlmuth, Barbara I. 15 Yang, Yidu 14 Funken, Stefan A. 14 Hackl, Klaus 14 Huang, Yunqing 14 Peterseim, Daniel 14 Repin, Sergeĭ Igorevich 13 Maischak, Matthias 13 Milošević, Dušan M. 13 Reddy, B. Dayanand 13 Roubíček, Tomáš 13 Xie, Xiaoping 12 Gallistl, Dietmar 12 Schroder, Andreas 11 Conti, Sergio 11 Dolzmann, Georg 11 Li, Jichun 11 Miehe, Christian 11 Nicaise, Serge 11 Ruiz-Baier, Ricardo 10 Banz, Lothar 10 Bi, Hai 10 Chen, Yanping 10 Hoppe, Ronald H. W. 10 Lamichhane, Bishnu Prasad 10 Melenk, Jens Markus 10 Merdon, Christian 10 Rančić, Lidija Z. 10 Stenberg, Rolf 10 Wriggers, Peter 9 Ainsworth, Mark 9 Aurada, Markus 9 Chen, Long 9 Erath, Christoph 9 Gantner, Gregor 9 Gopalakrishnan, Jay 9 Li, Jian 9 Meddahi, Salim 9 Nochetto, Ricardo Horacio 8 Barrios, Tomás P. 8 Beirão da Veiga, Lourenço 8 Du, Shaohong 8 González, María Paula 8 Haberl, Alexander 8 Hintermüller, Michael 8 Kochmann, Dennis M. 8 Oyarzúa, Ricardo 8 Petković, Ljiljana D. 8 Sayas, Francisco-Javier 8 Shi, Zhongci 8 Stein, Erwin 8 Xu, Jinchao 7 Bi, Chunjia 7 Cai, Zhiqiang 7 Chen, Shaochun 7 Chen, Zhangxin 7 Dond, Asha K. 7 Eigel, Martin 7 Ferraz-Leite, Samuel 7 Han, Weimin 7 Herceg, Đorđe D. 7 Hinze, Michael 7 Hsiao, George C. 7 Kim, Kwang Yeon 7 Larson, Mats G. 7 Li, Zhiping 7 Lin, Yanping 7 Liu, Jiangguo 7 Lu, Zuliang 7 Målqvist, Axel 7 Migórski, Stanisław 7 Nataraj, Neela 7 Prohl, Andreas 7 Rodríguez, Rodolfo 7 Wick, Thomas 7 Zhao, Lina 7 Zhao, Xin 7 Zhou, Aihui 7 Zou, Qingsong 6 Bertrand, Fleurianne ...and 1,623 more Authors all top 5 Cited in 178 Serials 183 Computer Methods in Applied Mechanics and Engineering 119 Numerische Mathematik 96 Journal of Computational and Applied Mathematics 89 Computers & Mathematics with Applications 68 Journal of Scientific Computing 67 Mathematics of Computation 60 Applied Numerical Mathematics 49 SIAM Journal on Numerical Analysis 43 Computational Methods in Applied Mathematics 38 Numerical Methods for Partial Differential Equations 35 Applied Mathematics and Computation 31 International Journal for Numerical Methods in Engineering 30 Computational Mechanics 27 Journal of Computational Physics 27 SIAM Journal on Scientific Computing 27 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 26 M\(^3\)AS. 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Académie des Sciences, Paris 2 Central European Journal of Mathematics 2 Multiscale Modeling & Simulation 2 Structural and Multidisciplinary Optimization ...and 78 more Serials all top 5 Cited in 42 Fields 1,190 Numerical analysis (65-XX) 529 Partial differential equations (35-XX) 503 Mechanics of deformable solids (74-XX) 202 Fluid mechanics (76-XX) 171 Calculus of variations and optimal control; optimization (49-XX) 68 Optics, electromagnetic theory (78-XX) 58 Functions of a complex variable (30-XX) 48 Field theory and polynomials (12-XX) 32 Real functions (26-XX) 23 Approximations and expansions (41-XX) 22 Integral equations (45-XX) 22 Statistical mechanics, structure of matter (82-XX) 20 Operator theory (47-XX) 18 Operations research, mathematical programming (90-XX) 17 Computer science (68-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Classical thermodynamics, heat transfer (80-XX) 10 Potential theory (31-XX) 9 Functional analysis (46-XX) 9 Probability theory and stochastic processes (60-XX) 9 Information and communication theory, circuits (94-XX) 8 Biology and other natural sciences (92-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 General and overarching topics; collections (00-XX) 6 Ordinary differential equations (34-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Mechanics of particles and systems (70-XX) 5 Quantum theory (81-XX) 4 Geophysics (86-XX) 3 History and biography (01-XX) 3 Commutative algebra (13-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year