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 32 articles )

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  1. Boffi, Daniele; Di Pietro, Daniele A.: Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes (2018)
  2. Ku, Jaeun; Reichel, Lothar: Simple efficient solvers for certain ill-conditioned systems of linear equations, including (H(\operatornamediv)) problems (2018)
  3. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes (2018)
  4. Deckelnick, Klaus; Hinze, Michael; Jordan, Tobias: An optimal shape design problem for plates (2017)
  5. Hintermüller, M.; Rautenberg, C. N.; Rösel, S.: Density of convex intersections and applications (2017)
  6. Liu, D. J.; Jiang, D. D.; Liu, Y.; Xia, Q. Q.: Stabilized FEM for some optimal design problem (2017)
  7. Sutton, Oliver J.: The virtual element method in 50 lines of MATLAB (2017)
  8. Acharya, Sanjib Kumar; Patel, Ajit: Primal hybrid method for parabolic problems (2016)
  9. Carstensen, Carsten; Dond, Asha K.; Nataraj, Neela; Pani, Amiya K.: Error analysis of nonconforming and mixed FEMs for second-order linear non-selfadjoint and indefinite elliptic problems (2016)
  10. Carstensen, Carsten; Peterseim, Daniel; Schröder, Andreas: The norm of a discretized gradient in (H(\mathrmdiv)^*) for a posteriori finite element error analysis (2016)
  11. Herzog, Roland; Mach, Susann: Preconditioned solution of state gradient constrained elliptic optimal control problems (2016)
  12. Lin, Mabelle; Mauroy, Benjamin; James, Joanna L.; Tawhai, Merryn H.; Clark, Alys R.: A multiscale model of placental oxygen exchange: the effect of villous tree structure on exchange efficiency (2016)
  13. Anjam, I.; Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements (2015)
  14. Carstensen, C.; Liu, D. J.: Nonconforming FEMs for an optimal design problem (2015)
  15. Lin, Guang; Liu, Jiangguo; Sadre-Marandi, Farrah: A comparative study on the weak Galerkin, discontinuous Galerkin, and mixed finite element methods (2015)
  16. Yang, Min; Liu, Jiangguo; Lin, Yanping: Pressure recovery for weakly over-penalized discontinuous Galerkin methods for the Stokes problem (2015)
  17. Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu: Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity (2014)
  18. Park, Eun-Jae; Seo, Boyoon: An upstream pseudostress-velocity mixed formulation for the Oseen equations (2014)
  19. Mu, Lin; Wang, Junping; Wang, Yanqiu; Ye, Xiu: A computational study of the weak Galerkin method for second-order elliptic equations (2013)
  20. Ervin, V. J.: Computational bases for (RT_k) and (BDM_k) on triangles (2012)

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