mfem swMATH ID: 22316 Software Authors: Carstensen, C; Bahriawati, C Description: Three Matlab implementations of the lowest-order Raviart-Thomas MFEM with a posteriori error control. The numerical approximation of the Laplace equation with inhomogeneous mixed boundary conditions in 2D with lowest-order Raviart-Thomas mixed finite elements is realized in three flexible and short MATLAB programs. The first, hybrid, implementation (LMmfem) is based on Lagrange multiplier techniques. The second, direct, approach (EBmfem) utilizes edge-basis functions for the lowest order Raviart-Thomas finite elements. The third ansatz (CRmfem) utilizes the P1 nonconforming finite element method due to Crouzeix and Raviart and then postprocesses the discrete flux via a technique due to Marini. It is the aim of this paper to derive, document, illustrate, and validate the three MATLAB implementations EBmfem, LMmfem, and CRmfem for further use and modification in education and research. A posteriori error control with a reliable and efficient averaging technique is included to monitor the discretization error. Therein, emphasis is on the correct treatment of mexed boundary conditions. Numerical examples illustrate some applications of the provided software and the quality of the error estimation. Homepage: https://www.math.hu-berlin.de/~cc/cc_homepage/software/software.shtml Dependencies: Matlab Related Software: Matlab; na14; iFEM; p1afem; AGMG; DistMesh; FreeFem++; NGSolve; Hermes2D; IGABEM2D; Bembel; ARPACK; HILBERT; Algorithm 949; FESTUNG; VTK; ParaView; Octave; Gmsh; SLEPc Cited in: 51 Publications all top 5 Cited by 97 Authors 8 Carstensen, Carsten 4 Liu, Jiangguo 3 Hoppe, Ronald H. W. 2 Chen, Huangxin 2 Deckelnick, Klaus 2 Hinze, Michael 2 Huyghe, Jacques M. 2 Ku, Jaeun 2 Lin, Guang 2 Majumder, Papri 2 Malakpoor, Kamyar 2 Mu, Lin 2 Praetorius, Dirk 2 Rautenberg, Carlos N. 2 Reichel, Lothar 2 Valdman, Jan 2 Ye, Xiu 2 Yu, Cong 1 Acharya, Sanjib Kumar 1 Aizinger, Vadym 1 Anjam, Immanuel 1 Arbogast, Todd 1 Bahriawati, C. 1 Barrett, John William 1 Bertrand, Fleurianne 1 Boffi, Daniele 1 Bringedal, Carina 1 Cai, Zhiqiang 1 Cirpka, Olaf A. 1 Clark, Alys R. 1 Di Pietro, Daniele Antonio 1 Dond, Asha K. 1 Ervin, Vincent J. 1 Frank, Florian 1 Gantner, Gregor 1 Gudi, Thirupathi 1 Günther, Andreas 1 Günther, David 1 He, Cuiyu 1 Herzog, Roland 1 Hintermüller, Michael 1 Huang, Yunqing 1 James, Joanna L. 1 Jordan, Tobias 1 Knabner, Peter 1 Kober, Bernhard 1 Kunisch, Karl 1 Kurz, Stefan 1 Li, Jichun 1 Lin, Mabelle 1 Lin, Yanping 1 Liu, Dongjie 1 Liu, Yang 1 Mach, Susann 1 Mauroy, Benjamin 1 Menaldi, Jose-Luis 1 Moldenhauer, Marcel 1 Morales, Fernando A. 1 Nataraj, Neela 1 Olivares, Manuela Bastidas 1 Pan, Hao 1 Pani, Amiya Kumar 1 Park, Eun-Jae 1 Patel, Ajit 1 Pauly, Dirk 1 Peralta, Gilbert R. 1 Peterseim, Daniel 1 Pop, Iuliu Sorin 1 Prigozhin, Leonid B. 1 Rabus, Hella 1 Reininghaus, Jan 1 Repin, Sergeĭ Igorevich 1 Reuter, Balthasar 1 Rösel, S. 1 Rui, Hongxing 1 Rüter, Marcus Olavi 1 Sadre-Marandi, Farrah 1 Schimanko, Stefan 1 Schroder, Andreas 1 Sebastian, Daniel 1 Selzer, Philipp 1 Seo, Boyoon 1 Starke, Gerhard 1 Stenberg, Rolf 1 Storn, Johannes 1 Sun, Shuyu 1 Sun, Weiwei 1 Sutton, Oliver J. 1 Tavener, Simon J. 1 Tawhai, Merryn H. 1 Thiele, Jan 1 Wang, Junping 1 Wang, Yanqiu 1 Wang, Zhuoran 1 Xu, Xuejun 1 Yang, Min 1 Zhang, Shun all top 5 Cited in 23 Serials 8 Numerische Mathematik 4 SIAM Journal on Numerical Analysis 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational and Applied Mathematics 3 Computational Mechanics 3 Journal of Scientific Computing 3 Computational Methods in Applied Mathematics 2 Computers & Mathematics with Applications 2 Journal of Computational Physics 2 Mathematics of Computation 2 Applied Mathematics and Computation 2 Applied Numerical Mathematics 2 Numerical Algorithms 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Bulletin of the Korean Mathematical Society 1 International Journal of Computer Mathematics 1 Computational and Applied Mathematics 1 Journal of Convex Analysis 1 Computational Geosciences 1 Advances in Numerical Analysis 1 Advances in Applied Mathematics and Mechanics 1 Journal of Theoretical Biology 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Cited in 10 Fields 46 Numerical analysis (65-XX) 22 Partial differential equations (35-XX) 13 Fluid mechanics (76-XX) 8 Mechanics of deformable solids (74-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 2 Operations research, mathematical programming (90-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year