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.

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  2. Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel: Functional a posteriori error estimates for boundary element methods (2021)
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  4. Gudi, Thirupathi; Majumder, Papri: Crouzeix-Raviart finite element approximation for the parabolic obstacle problem (2020)
  5. Ku, JaEun; Reichel, Lothar: A novel iterative method for discrete Helmholtz decomposition (2020)
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  8. Yu, Cong; Malakpoor, Kamyar; Huyghe, Jacques M.: Comparing mixed hybrid finite element method with standard FEM in swelling simulations involving extremely large deformations (2020)
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  13. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes (2018)
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