mfem

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.


References in zbMATH (referenced in 50 articles )

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  1. Peralta, Gilbert; Kunisch, Karl: Mixed and hybrid Petrov-Galerkin finite element discretization for optimal control of the wave equation (2022)
  2. Sun, Weiwei: New analysis and recovery technique of mixed FEMs for compressible miscible displacement in porous media (2022)
  3. Bastidas Olivares, Manuela; Bringedal, Carina; Pop, Iuliu Sorin: A two-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media (2021)
  4. Chen, Huangxin; Sun, Shuyu: A new physics-preserving IMPES scheme for incompressible and immiscible two-phase flow in heterogeneous porous media (2021)
  5. Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel: Functional a posteriori error estimates for boundary element methods (2021)
  6. Majumder, Papri: A convergence analysis of semi-discrete and fully-discrete nonconforming FEM for the parabolic obstacle problem (2021)
  7. Menaldi, José-Luis; Rautenberg, Carlos N.: On some quasi-variational inequalities and other problems with moving sets (2021)
  8. Bertrand, Fleurianne; Kober, Bernhard; Moldenhauer, Marcel; Starke, Gerhard: Equilibrated stress reconstruction and a posteriori error estimation for linear elasticity (2020)
  9. Gudi, Thirupathi; Majumder, Papri: Crouzeix-Raviart finite element approximation for the parabolic obstacle problem (2020)
  10. Ku, JaEun; Reichel, Lothar: A novel iterative method for discrete Helmholtz decomposition (2020)
  11. Selzer, Philipp; Cirpka, Olaf A.: Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow (2020)
  12. Storn, Johannes: Computation of the LBB constant for the Stokes equation with a least-squares finite element method (2020)
  13. Yu, Cong; Malakpoor, Kamyar; Huyghe, Jacques M.: Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations (2020)
  14. Morales, Fernando A.: A conforming primal-dual mixed formulation for the 2D multiscale porous media flow problem (2019)
  15. Yu, Cong; Malakpoor, Kamyar; Huyghe, Jacques M.: A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels (2019)
  16. Boffi, Daniele; Di Pietro, Daniele A.: Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes (2018)
  17. Ku, Jaeun; Reichel, Lothar: Simple efficient solvers for certain ill-conditioned systems of linear equations, including (H(\operatornamediv)) problems (2018)
  18. Liu, D. J.; Li, A. Q.; Chen, Z. R.: Nonconforming FEMs for the (p)-Laplace problem (2018)
  19. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes (2018)
  20. Cai, Zhiqiang; He, Cuiyu; Zhang, Shun: Improved ZZ a posteriori error estimators for diffusion problems: conforming linear elements (2017)

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