Edit Profile (opens in new tab) Carstensen, Carsten Compute Distance To: Compute Author ID: carstensen.carsten Published as: Carstensen, Carsten; Carstensen, C. Homepage: http://www2.mathematik.hu-berlin.de/~cc/cc_homepage/cc/education.shtml External Links: MGP · Google Scholar · ResearchGate · dblp · GND Documents Indexed: 278 Publications since 1987, including 1 Book 14 Contributions as Editor Co-Authors: 128 Co-Authors with 244 Joint Publications 3,504 Co-Co-Authors all top 5 Co-Authors 42 single-authored 16 Funken, Stefan A. 13 Gallistl, Dietmar 12 Bartels, Sören 12 Gedicke, Joscha 11 Nataraj, Neela 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 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 Pani, Amiya Kumar 5 Park, Eun-Jae 5 Weinberg, Kerstin 5 Zarrabi, Darius 4 Braess, Dietrich 4 Demkowicz, Leszek F. 4 Stein, Erwin 3 Beckermann, Bernhard 3 Dond, Asha K. 3 Eigel, Martin 3 Hoppe, Ulrich 3 Köhler, Karoline 3 Prohl, Andreas 3 Puttkammer, Sophie 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 Ern, Alexandre 2 Gopalakrishnan, Jay 2 Günther, David 2 Gwinner, Joachim 2 Hecht, Axel 2 Jansche, Stefan 2 Jensen, Max 2 Liu, Dongjie 2 Liu, Steve Wenbin 2 Ma, Rui 2 Maischak, Matthias 2 Mallik, Gouranga 2 Mehrmann, Volker 2 Międlar, Agnieszka 2 Monk, Peter B. 2 Mühlbach, Günter W. 2 Sauter, Stefan A. 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 Boffi, Daniele 1 Brink, Ulrich 1 Buffa, Annalisa 1 Carstensen, Christine 1 Causin, Paola 1 Dörfler, Willibald 1 Ebobisse, François Bille 1 Estep, Donald J. 1 Faermann, Birgit 1 Feischl, Michael 1 Gaddam, Sharat 1 Gerritsma, Marc I. 1 Gudi, Thirupathi 1 Hackbusch, Wolfgang 1 Helm, D. S. 1 Huang, Yunqing 1 Huth, Robert 1 Jochimsen, K. 1 Kim, Dongho 1 Krämer, Boris 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 ...and 28 more Co-Authors all top 5 Serials 48 Numerische Mathematik 38 SIAM Journal on Numerical Analysis 18 Computer Methods in Applied Mechanics and Engineering 18 Mathematics of Computation 11 Computers & Mathematics with Applications 10 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 10 Oberwolfach Reports 9 IMA Journal of Numerical Analysis 9 Computational Methods in Applied Mathematics 7 SIAM Journal on Scientific Computing 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 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 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 Babeș-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 GAMM-Mitteilungen 1 CISM International Centre for Mechanical Sciences. Courses and Lectures 1 Lecture Notes in Computational Science and Engineering all top 5 Fields 242 Numerical analysis (65-XX) 110 Mechanics of deformable solids (74-XX) 99 Partial differential equations (35-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 19 Fluid mechanics (76-XX) 15 Functions of a complex variable (30-XX) 14 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 Potential theory (31-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 1 Number theory (11-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 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 248 Publications have been cited 3,623 times in 1,763 Documents Cited by ▼ Year ▼ A posteriori error estimate for the mixed finite element method. Zbl 0864.65068Carstensen, Carsten 130 1997 Non-convex potentials and microstructures in finite-strain plasticity. Zbl 1008.74016Carstensen, Carsten; Hackl, Klaus; Mielke, Alexander 122 2002 Axioms of adaptivity. Zbl 1350.65119Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. 95 2014 Edge residuals dominate a posteriori error estimates for low order finite element methods. Zbl 0938.65124Carstensen, Carsten; Verfürth, Rüdiger 78 1999 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 75 2002 Breaking spaces and forms for the DPG method and applications including Maxwell equations. Zbl 1359.65249Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. 72 2016 Quasi-interpolation and a posteriori error analysis in finite element methods. Zbl 0948.65113Carstensen, Carsten 67 1999 Remarks around 50 lines of Matlab: short finite element implementation. Zbl 0938.65129Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A. 63 1999 A posteriori error estimates for mixed FEM in elasticity. Zbl 0928.74093Carstensen, Carsten; Dolzmann, Georg 55 1998 An a posteriori error estimate for a first-kind integral equation. Zbl 0854.65102Carstensen, Carsten 50 1997 A unifying theory of a posteriori error control for nonconforming finite element methods. Zbl 1127.65083Carstensen, C.; Hu, Jun 50 2007 A posteriori error estimates for nonconforming finite element methods. Zbl 1010.65044Carstensen, Carsten; Bartels, Sören; Jansche, Stefan 49 2002 Three Matlab implementations of the lowest-order Raviart-Thomas MFEM with a posteriori error control. Zbl 1086.65107Bahriawati, C.; Carstensen, C. 48 2005 A unifying theory of a posteriori finite element error control. Zbl 1100.65089Carstensen, C. 45 2005 Framework for the a posteriori error analysis of nonconforming finite elements. Zbl 1165.65072Carstensen, Carsten; Hu, Jun; Orlando, Antonio 43 2007 Guaranteed lower bounds for eigenvalues. Zbl 1320.65162Carstensen, Carsten; Gedicke, Joscha 42 2014 Error reduction and convergence for an adaptive mixed finite element method. Zbl 1094.65112Carstensen, Carsten; Hoppe, R. H. W. 42 2006 Averaging techniques yield reliable a posteriori finite element error control for obstacle problems. Zbl 1063.65050Bartels, S.; Carstensen, C. 40 2004 Numerical solution of the scalar double-well problem allowing microstructure. Zbl 0870.65055Carstensen, Carsten; Plechác, Petr 38 1997 A posteriori error control for DPG methods. Zbl 1320.65171Carstensen, Carsten; Demkowicz, Leszek; Gopalakrishnan, Jay 38 2014 A posteriori error estimate and h-adaptive algorithm on surfaces from Symm’s integral equation. Zbl 1018.65138Carstensen, C.; Maischak, M.; Stephan, E. P. 37 2001 Fully reliable localized error control in the FEM. Zbl 0956.65099Carstensen, Carsten; Funken, Stefan A. 37 2000 A posteriori error estimates for boundary element methods. Zbl 0831.65120Carstensen, Carsten; Stephan, Ernst P. 36 1995 Convergence analysis of an adaptive nonconforming finite element method. Zbl 1101.65102Carstensen, Carsten; Hoppe, Ronald H. W. 36 2006 Effective relaxation for microstructure simulations: algorithms and applications. Zbl 1112.74501Bartels, S.; Carstensen, C.; Hackl, K.; Hoppe, U. 35 2004 Weierstrass formula and zero-finding methods. Zbl 0821.65028Petković, Miodrag S.; Carstensen, Carsten; Trajkovíc, Miroslav 34 1995 Constants in Clément-interpolation error and residual based a posteriori error estimates in finite element methods. Zbl 0973.65091Carstensen, C.; Funken, S. A. 34 2000 Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. Zbl 1062.65113Bartels, S.; Carstensen, C.; Dolzmann, G. 34 2004 Convergence analysis of a conforming adaptive finite element method for an obstacle problem. Zbl 1126.65058Braess, Dietrich; Carstensen, Carsten; Hoppe, Ronald H. W. 34 2007 Guaranteed lower eigenvalue bounds for the biharmonic equation. Zbl 1298.65165Carstensen, Carsten; Gallistl, Dietmar 34 2014 A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems. Zbl 1014.76042Carstensen, Carsten; Funken, Stefan A. 31 2001 Matlab implementation of the finite element method in elasticity. Zbl 1239.74092Alberty, Jochen; Carstensen, Carsten; Funken, Stefan A.; Klose, Roland 31 2002 Adaptive numerical analysis in primal elastoplasticity with hardening. Zbl 0956.74049Alberty, Jochen; Carstensen, Carsten; Zarrabi, Darius 30 1999 Averaging technique for FE – a posteriori error control in elasticity. I: Conforming FEM. Zbl 0981.74063Carstensen, Carsten; Funken, Stefan A. 29 2001 Explicit and averaging a posteriori error estimates for adaptive finite volume methods. Zbl 1084.65112Carstensen, C.; Lazarov, R.; Tomov, S. 28 2005 Residual-based a posteriori error estimate for hypersingular equation on surfaces. Zbl 1063.65116Carstensen, Carsten; Maischak, M.; Praetorius, D.; Stephan, E. P. 28 2004 An oscillation-free adaptive FEM for symmetric eigenvalue problems. Zbl 1227.65106Carstensen, Carsten; Gedicke, Joscha 27 2011 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 27 2002 Local stress regularity in scalar nonconvex variational problems. Zbl 1012.49027Carstensen, Carsten; Müller, Stefan 25 2002 Adaptive coupling of boundary elements and finite elements. Zbl 0849.65083Carstensen, Carsten; Stephan, Ernst P. 25 1995 Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods. Zbl 1274.65290Carstensen, Carsten; Gedicke, Joscha; Rim, Donsub 25 2012 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 25 2011 Some improved inclusion methods for polynomial roots with Weierstrass’ corrections. Zbl 0776.65036Petković, Miodrag S.; Carstensen, Carsten 24 1993 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 Adaptive boundary element methods for some first kind integral equations. Zbl 0863.65073Carstensen, Carsten; Stephan, Ernst P. 24 1996 Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. Zbl 1105.65124Carstensen, Carsten; Praetorius, Dirk 24 2006 An adaptive mesh-refining algorithm allowing for an \(H^1\) stable \(L^2\) projection onto Courant finite element spaces. Zbl 1064.65143Carstensen, Carsten 23 2004 A review of unified a posteriori finite element error control. Zbl 1289.65249Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 23 2012 Numerical approximation of Young measures in non-convex variational problems. Zbl 0945.65070Carstensen, Carsten; Roubíček, Tomáš 22 2000 A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems. Zbl 0954.65052Carstensen, Carsten; Gwinner, Joachim 22 1999 Axioms of adaptivity with separate marking for data resolution. Zbl 1377.65147Carstensen, C.; Rabus, H. 21 2017 On the adaptive coupling of FEM and BEM in 2-d elasticity. Zbl 0880.73062Carstensen, C.; Funken, S. A.; Stephan, E. P. 21 1997 Comparison results of finite element methods for the Poisson model problem. Zbl 1261.65115Carstensen, C.; Peterseim, D.; Schedensack, M. 21 2012 Adaptive finite elements for elastic bodies in contact. Zbl 0940.74058Carstensen, C.; Scherf, O.; Wriggers, P. 21 1999 An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity. Zbl 1254.65123Carstensen, Carsten; Gedicke, Joscha 21 2012 All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable. Zbl 1067.65115Carstensen, C. 21 2004 The arnold-winther mixed FEM in linear elasticity. I: Implementation and numerical verification. Zbl 1194.74374Carstensen, C.; Günther, D.; Reininghaus, J.; Thiele, J. 20 2008 Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis. Zbl 1073.65120Carstensen, Carsten 20 2004 Numerical analysis of the primal problem of elastoplasticity with hardening. Zbl 0947.74061Carstensen, Carsten 20 1999 Efficiency of a posteriori BEM-error estimates for first-kind integral equations on quasi-uniform meshes. Zbl 0849.65084Carstensen, Carsten 20 1996 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 A unifying theory of a posteriori error control for discontinuous Galerkin FEM. Zbl 1169.65106Carstensen, Carsten; Gudi, Thirupathi; Jensen, Max 19 2009 Convergence and optimality of adaptive least squares finite element methods. Zbl 1327.65212Carstensen, Carsten; Park, Eun-Jae 19 2015 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. 18 2001 Optimal adaptive nonconforming FEM for the Stokes problem. Zbl 1316.76046Carstensen, Carsten; Peterseim, Daniel; Rabus, Hella 17 2013 Locking-free adaptive mixed finite element methods in linear elasticity. Zbl 1004.74068Carstensen, C.; Dolzmann, G.; Funken, S. A.; Helm, D. S. 17 2000 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 An optimal adaptive mixed finite element method. Zbl 1215.65173Carstensen, Carsten; Rabus, Hella 17 2011 A posteriori finite element error control for the \(p\)-Laplace problem. Zbl 1050.65101Carstensen, Carsten; Klose, R. 17 2003 On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials. Zbl 0779.65030Carstensen, Carsten 16 1993 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 Hanging nodes in the unifying theory of a posteriori finite element error control. Zbl 1212.65423Carstensen, C.; Hu, Jun 16 2009 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172Carstensen, C.; Eigel, M.; Gedicke, J. 16 2011 Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Zbl 1311.65136Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 16 2015 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 15 2014 Numerical analysis of compatible phase transitions in elastic solids. Zbl 1049.74062Carstensen, Carsten; Plechác, Petr 15 2000 Estimator competition for Poisson problems. Zbl 1224.65253Carstensen, C.; Merdon, C. 15 2010 Elastoviscoplastic finite element analysis in 100 lines of Matlab. Zbl 1099.74544Carstensen, C.; Klose, R. 15 2002 Adaptive finite element methods for microstructures? Numerical experiments for a 2-well benchmark. Zbl 1090.74054Carstensen, C.; Jochimsen, K. 15 2003 Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. Zbl 1457.65185Carstensen, C.; Hellwig, F. 15 2016 Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. Zbl 1007.74062Carstensen, Carsten; Plecháč, Petr 14 2001 Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations. Zbl 1073.78008Carstensen, C.; Hoppe, R. H. W. 14 2005 Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. Zbl 1285.65079Carstensen, C.; Merdon, C. 14 2013 A posteriori error estimators for convection-diffusion eigenvalue problems. Zbl 1295.65108Gedicke, J.; Carstensen, C. 14 2014 Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics. Zbl 0877.73063Brink, Ulrich; Carstensen, Carsten; Stein, Erwin 14 1996 Quasi-optimal adaptive pseudostress approximation of the Stokes equations. Zbl 1383.76333Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 14 2013 FEM and BEM coupling for a nonlinear transmission problem with Signorini contact. Zbl 0896.65079Carstensen, Carsten; Gwinner, Joachim 13 1997 Adaptive finite element analysis of geometrically nonlinear plates and shells, especially buckling. Zbl 0809.73072Stein, Erwin; Seifert, B.; Ohnimus, S.; Carstensen, Carsten 13 1994 Medius analysis and comparison results for first-order finite element methods in linear elasticity. Zbl 1329.74272Carstensen, C.; Schedensack, M. 13 2015 On iteration methods without derivatives for the simultaneous determination of polynomial zeros. Zbl 0776.65033Carstensen, Carsten; Petković, Miodrag S. 12 1993 A posteriori FE error control for \(p\)-Laplacian by gradient recovery in quasi-norm. Zbl 1121.65111Carstensen, Carsten; Liu, W.; Yan, N. 12 2006 Residual-based a posteriori error estimate for a nonconforming Reissner–Mindlin plate finite element. Zbl 1042.74049Carstensen, Carsten 12 2002 Low-order dPG-FEM for an elliptic PDE. Zbl 1364.65242Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L. 12 2014 Inclusion of the roots of a polynomial based on Gerschgorin’s theorem. Zbl 0726.65053Carstensen, C. 12 1991 A posteriori error estimate for the symmetric coupling of finite elements and boundary elements. Zbl 0863.65070Carstensen, C. 12 1996 An adaptive homotopy approach for non-selfadjoint eigenvalue problems. Zbl 1263.65106Carstensen, Carsten; Gedicke, Joscha; Mehrmann, Volker; Miedlar, Agnieszka 12 2011 An experimental survey of a posteriori Courant finite element error control for the Poisson equation. Zbl 0999.65117Carstensen, Carsten; Bartels, Sören; Klose, Roland 11 2001 Adaptive techniques for the contact of elastic bodies. Zbl 1122.74528Wriggers, P.; Scherf, O.; Carstensen, C. 11 1994 Linear construction of companion matrices. Zbl 0717.15011Carstensen, C. 11 1991 Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity. Zbl 1460.65145Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 6 2021 Adaptive Morley FEM for the von Kármán equations with optimal convergence rates. Zbl 1467.65107Carstensen, Carsten; Nataraj, Neela 2 2021 Adaptive mixed finite element methods for non-self-adjoint indefinite second-order elliptic PDEs with optimal rates. Zbl 1468.65185Carstensen, Carsten; Ma, Rui 1 2021 Collective marking for arbitrary order adaptive least-squares finite element methods with optimal rates. Zbl 07362365Carstensen, Carsten; Ma, Rui 1 2021 Morley finite element method for the von Kármán obstacle problem. Zbl 07420191Carstensen, Carsten; Gaddam, Sharat; Nataraj, Neela; Pani, Amiya K.; Shylaja, Devika 1 2021 A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides. Zbl 1476.65294Carstensen, Carsten; Nataraj, Neela 1 2021 How to prove the discrete reliability for nonconforming finite element methods. Zbl 1463.65362Carstensen, Carsten; Puttkammer, Sophie 6 2020 Collective marking for adaptive least-squares finite element methods with optimal rates. Zbl 1426.65171Carstensen, Carsten 4 2020 A skeletal finite element method can compute lower eigenvalue bounds. Zbl 1475.65178Carstensen, Carsten; Zhai, Qilong; Zhang, Ran 2 2020 A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations. Zbl 1465.65129Carstensen, Carsten; Mallik, Gouranga; Nataraj, Neela 8 2019 Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM. Zbl 1426.65162Carstensen, Carsten; Gallistl, Dietmar; Gedicke, Joscha 4 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 3 2019 Nonlinear discontinuous Petrov-Galerkin methods. Zbl 1398.65292Carstensen, C.; Bringmann, P.; Hellwig, F.; Wriggers, P. 10 2018 An adaptive least-squares FEM for linear elasticity with optimal convergence rates. Zbl 1462.65179Bringmann, P.; Carstensen, C.; Starke, Gerhard 8 2018 Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation. Zbl 1401.65130Carstensen, Carsten; Hellwig, Friederike 7 2018 Asymptotic exactness of the least-squares finite element residual. Zbl 1397.65230Carstensen, Carsten; Storn, Johannes 5 2018 A low-order discontinuous Petrov-Galerkin method for the Stokes equations. Zbl 1401.65131Carstensen, Carsten; Puttkammer, Sophie 4 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. 3 2018 Optimal convergence rates for adaptive lowest-order discontinuous Petrov-Galerkin schemes. Zbl 1395.65140Carstensen, Carsten; Hellwig, Friederike 2 2018 Axioms of adaptivity with separate marking for data resolution. Zbl 1377.65147Carstensen, C.; Rabus, H. 21 2017 Convergence of natural adaptive least squares finite element methods. Zbl 1378.65176Carstensen, Carsten; Park, Eun-Jae; Bringmann, Philipp 9 2017 Nonconforming FEM for the obstacle problem. Zbl 1433.65284Carstensen, C.; Köhler, K. 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. 3 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. 2 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 Breaking spaces and forms for the DPG method and applications including Maxwell equations. Zbl 1359.65249Carstensen, C.; Demkowicz, L.; Gopalakrishnan, J. 72 2016 Low-order discontinuous Petrov-Galerkin finite element methods for linear elasticity. Zbl 1457.65185Carstensen, C.; Hellwig, F. 15 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. 11 2016 \(L^{2}\) best approximation of the elastic stress in the Arnold-Winther FEM. Zbl 1433.74102Carstensen, C.; Gallistl, D.; Schedensack, M. 9 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. 7 2016 Justification of the saturation assumption. Zbl 1348.65161Carstensen, C.; Gallistl, D.; Gedicke, J. 5 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 5 2016 Guaranteed velocity error control for the pseudostress approximation of the Stokes equations. Zbl 1401.76083Bringmann, P.; Carstensen, C.; Merdon, C. 4 2016 Robust residual-based a posteriori Arnold-winther mixed finite element analysis in elasticity. Zbl 1425.74455Carstensen, Carsten; Gedicke, Joscha 2 2016 A natural nonconforming FEM for the Bingham flow problem is quasi-optimal. Zbl 1457.65186Carstensen, C.; Reddy, B. D.; Schedensack, M. 2 2016 Convergence and optimality of adaptive least squares finite element methods. Zbl 1327.65212Carstensen, Carsten; Park, Eun-Jae 19 2015 Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Zbl 1311.65136Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 16 2015 Medius analysis and comparison results for first-order finite element methods in linear elasticity. Zbl 1329.74272Carstensen, C.; Schedensack, M. 13 2015 Nonconforming FEMs for an optimal design problem. Zbl 1312.74036Carstensen, C.; Liu, D. J. 8 2015 An optimal adaptive finite element method for an obstacle problem. Zbl 1317.65232Carstensen, Carsten; Hu, Jun 5 2015 Comparison results for the Stokes equations. Zbl 1320.76062Carstensen, C.; Köhler, K.; Peterseim, D.; Schedensack, M. 5 2015 Comparison results of nonstandard \(P_2\) finite element methods for the biharmonic problem. Zbl 1327.65211Carstensen, Carsten; Gallistl, Dietmar; Nataraj, Neela 4 2015 Convergence of adaptive finite element methods for a nonconvex double-well minimization problem. Zbl 1329.74273Carstensen, Carsten; Dolzmann, Georg 1 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. 95 2014 Guaranteed lower bounds for eigenvalues. Zbl 1320.65162Carstensen, Carsten; Gedicke, Joscha 42 2014 A posteriori error control for DPG methods. Zbl 1320.65171Carstensen, Carsten; Demkowicz, Leszek; Gopalakrishnan, Jay 38 2014 Guaranteed lower eigenvalue bounds for the biharmonic equation. Zbl 1298.65165Carstensen, Carsten; Gallistl, Dietmar 34 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 15 2014 A posteriori error estimators for convection-diffusion eigenvalue problems. Zbl 1295.65108Gedicke, J.; Carstensen, C. 14 2014 Low-order dPG-FEM for an elliptic PDE. Zbl 1364.65242Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L. 12 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. 3 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 17 2013 Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. Zbl 1285.65079Carstensen, C.; Merdon, C. 14 2013 Quasi-optimal adaptive pseudostress approximation of the Stokes equations. Zbl 1383.76333Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 14 2013 Effective postprocessing for equilibration a posteriori error estimators. Zbl 1267.65162Carstensen, C.; Merdon, C. 8 2013 A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles. Zbl 1316.74060Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun 8 2013 Discrete reliability for Crouzeix-Raviart FEMs. Zbl 1321.65171Carstensen, Carsten; Gallistl, Dietmar; Schedensack, Mira 8 2013 A posteriori error estimator competition for conforming obstacle problems. Zbl 1364.65243Carstensen, C.; Merdon, C. 5 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 Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods. Zbl 1274.65290Carstensen, Carsten; Gedicke, Joscha; Rim, Donsub 25 2012 A review of unified a posteriori finite element error control. Zbl 1289.65249Carstensen, C.; Eigel, M.; Hoppe, R. H. W.; Löbhard, C. 23 2012 Comparison results of finite element methods for the Poisson model problem. Zbl 1261.65115Carstensen, C.; Peterseim, D.; Schedensack, M. 21 2012 An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity. Zbl 1254.65123Carstensen, Carsten; Gedicke, Joscha 21 2012 P\(_1\)-nonconforming finite elements on triangulations into triangles and quadrilaterals. Zbl 1251.65156Altmann, Robert; Carstensen, Carsten 9 2012 The adaptive nonconforming FEM for the pure displacement problem in linear elasticity is optimal and robust. Zbl 1397.74183Carstensen, Carsten; Rabus, Hella 9 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 4 2012 Numerical experiments for the Arnold-Einther mixed finite elements for the Stokes problem. Zbl 1250.76130Carstensen, Carsten; Gedicke, Joscha; Park, Eun-Jae 3 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 27 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 25 2011 An optimal adaptive mixed finite element method. Zbl 1215.65173Carstensen, Carsten; Rabus, Hella 17 2011 Computational competition of symmetric mixed FEM in linear elasticity. Zbl 1230.74172Carstensen, C.; Eigel, M.; Gedicke, J. 16 2011 An adaptive homotopy approach for non-selfadjoint eigenvalue problems. Zbl 1263.65106Carstensen, Carsten; Gedicke, Joscha; Mehrmann, Volker; Miedlar, Agnieszka 12 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 10 2011 Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods. Zbl 1230.74205Yu, Guozhu; Xie, Xiaoping; Carstensen, Carsten 9 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. 15 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. 3 2010 A unifying theory of a posteriori error control for discontinuous Galerkin FEM. Zbl 1169.65106Carstensen, Carsten; Gudi, Thirupathi; Jensen, Max 19 2009 Hanging nodes in the unifying theory of a posteriori finite element error control. Zbl 1212.65423Carstensen, C.; Hu, Jun 16 2009 Convergence of adaptive finite element methods in computational mechanics. Zbl 1419.74232Carstensen, Carsten 9 2009 Error reduction in adaptive finite element approximations of elliptic obstacle problems. Zbl 1212.65246Braess, Dietrich; Carstensen, Carsten; Hoppe, Ronald H. W. 8 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 1169.65002 3 2009 Lectures on adaptive mixed finite element methods. Zbl 1181.65136Carstensen, C. 2 2009 The arnold-winther mixed FEM in linear elasticity. I: Implementation and numerical verification. Zbl 1194.74374Carstensen, C.; Günther, D.; Reininghaus, J.; Thiele, J. 20 2008 Mixed analytical-numerical relaxation in finite single-slip crystal plasticity. Zbl 1160.74326Carstensen, Carsten; Conti, Sergio; Orlando, Antonio 11 2008 Convergence of an adaptive FEM for a class of degenerate convex minimization problems. Zbl 1169.65065Carstensen, Carsten 9 2008 A convergent adaptive finite element method for an optimal design problem. Zbl 1144.74038Bartels, Sören; Carstensen, Carsten 5 2008 A posteriori error analysis for conforming MITC elements for Reissner-Mindlin plates. Zbl 1130.74045Carstensen, C.; Hu, Jun 5 2008 Partition of unity for localization in implicit a posteriori finite element error control for linear elasticity. Zbl 1195.74166Carstensen, Carsten; Thiele, Jan 4 2008 ...and 148 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,812 Authors 133 Carstensen, Carsten 60 Praetorius, Dirk 44 Petković, Miodrag S. 43 Gatica, Gabriel N. 36 Stephan, Ernst Peter 28 Führer, Thomas 27 Demkowicz, Leszek F. 24 Vohralík, Martin 22 Mosler, Jörn 21 Feischl, Michael 20 Park, Eun-Jae 19 Bartels, Sören 19 Heuer, Norbert 19 Hu, Jun 19 Yang, Yidu 18 Karkulik, Michael 17 Ern, Alexandre 17 Repin, Sergeĭ Igorevich 16 Gedicke, Joscha 16 Gudi, Thirupathi 16 Mielke, Alexander 16 Valdman, Jan 16 Wohlmuth, Barbara I. 15 Funken, Stefan A. 15 Hackl, Klaus 15 Huang, Yunqing 15 Xie, Xiaoping 14 Peterseim, Daniel 13 Gallistl, Dietmar 13 Maischak, Matthias 13 Milošević, Dušan M. 13 Nataraj, Neela 13 Reddy, B. Dayanand 13 Roubíček, Tomáš 13 Ruiz-Baier, Ricardo 12 Conti, Sergio 12 Gantner, Gregor 12 Melenk, Jens Markus 12 Schroder, Andreas 11 Bi, Hai 11 Dolzmann, Georg 11 Hoppe, Ronald H. W. 11 Lamichhane, Bishnu Prasad 11 Miehe, Christian 11 Nicaise, Serge 11 Oyarzúa, Ricardo 10 Banz, Lothar 10 Chen, Yanping 10 Du, Shaohong 10 Hintermüller, Michael 10 Li, Jichun 10 Meddahi, Salim 10 Merdon, Christian 10 Rančić, Lidija Z. 10 Stenberg, Rolf 10 Wriggers, Peter 9 Ainsworth, Mark 9 Aurada, Markus 9 Barrios, Tomás P. 9 Bertrand, Fleurianne 9 Boffi, Daniele 9 Chen, Long 9 Erath, Christoph 9 Haberl, Alexander 9 Li, Jian 9 Nochetto, Ricardo Horacio 9 Stevenson, Rob P. 9 Wick, Thomas 9 Zhang, Zhimin 8 Beirão da Veiga, Lourenço 8 Cai, Zhiqiang 8 Han, Weimin 8 Herceg, Đorđe D. 8 Hsiao, George C. 8 Kochmann, Dennis M. 8 Liu, Jiangguo 8 Migórski, Stanisław 8 Petković, Ljiljana D. 8 Sayas, Francisco-Javier 8 Shi, Zhongci 8 Stein, Erwin 8 Xu, Jinchao 7 Bi, Chunjia 7 Chen, Shaochun 7 Chen, Zhangxin 7 Eigel, Martin 7 Ferraz-Leite, Samuel 7 Gopalakrishnan, Jay 7 Hinze, Michael 7 Kim, Kwang Yeon 7 Larson, Mats G. 7 Li, Hao 7 Li, Zhiping 7 Lin, Yanping 7 Lu, Zuliang 7 Ma, Rui 7 Målqvist, Axel 7 Mao, Shipeng 7 Neff, Patrizio 7 Ortiz, Michael ...and 1,712 more Authors all top 5 Cited in 198 Serials 193 Computer Methods in Applied Mechanics and Engineering 128 Numerische Mathematik 112 Computers & Mathematics with Applications 101 Journal of Computational and Applied Mathematics 72 Mathematics of Computation 71 Journal of Scientific Computing 67 Applied Numerical Mathematics 61 Computational Methods in Applied Mathematics 55 SIAM Journal on Numerical Analysis 41 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 38 Numerical Methods for Partial Differential Equations 36 Applied Mathematics and Computation 34 Computational Mechanics 32 Journal of Computational Physics 31 International Journal for Numerical Methods in Engineering 28 M\(^3\)AS. 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Solids 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Systems Science and Complexity 3 Multiscale Modeling & Simulation 3 International Journal of Numerical Analysis and Modeling 3 Oberwolfach Reports 3 Communications in Computational Physics 2 International Journal of Solids and Structures 2 Inverse Problems 2 Journal of Engineering Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Kybernetika 2 Mathematische Annalen 2 Meccanica 2 Mechanics Research Communications 2 Proceedings of the American Mathematical Society 2 Theoretical Computer Science 2 Zeitschrift für Analysis und ihre Anwendungen 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Constructive Approximation 2 Journal of Integral Equations and Applications 2 Science in China. Series A 2 Computational Mathematics and Modeling 2 SIAM Journal on Applied Mathematics 2 Mathematical Programming. Series A. Series B 2 SIAM Journal on Optimization 2 Journal of Nonlinear Science 2 Communications in Numerical Methods in Engineering ...and 98 more Serials all top 5 Cited in 42 Fields 1,359 Numerical analysis (65-XX) 616 Partial differential equations (35-XX) 546 Mechanics of deformable solids (74-XX) 238 Fluid mechanics (76-XX) 193 Calculus of variations and optimal control; optimization (49-XX) 76 Optics, electromagnetic theory (78-XX) 58 Functions of a complex variable (30-XX) 47 Field theory and polynomials (12-XX) 35 Real functions (26-XX) 27 Approximations and expansions (41-XX) 26 Statistical mechanics, structure of matter (82-XX) 23 Integral equations (45-XX) 23 Operator theory (47-XX) 22 Operations research, mathematical programming (90-XX) 21 Computer science (68-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Potential theory (31-XX) 13 Probability theory and stochastic processes (60-XX) 13 Classical thermodynamics, heat transfer (80-XX) 12 Functional analysis (46-XX) 10 Biology and other natural sciences (92-XX) 8 General and overarching topics; collections (00-XX) 8 Ordinary differential equations (34-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Information and communication theory, circuits (94-XX) 7 Quantum theory (81-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Mechanics of particles and systems (70-XX) 5 Geophysics (86-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Systems theory; control (93-XX) 3 History and biography (01-XX) 3 Commutative algebra (13-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Statistics (62-XX) 2 Combinatorics (05-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year