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MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs

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  • Innerberger, Michael
  • Praetorius, Dirk

Abstract

We present an easily accessible, object oriented code (written exclusively in Matlab) for adaptive finite element simulations in 2D. It features various refinement routines for triangular meshes as well as fully vectorized FEM ansatz spaces of arbitrary polynomial order and allows for problems with very general coefficients. In particular, our code can handle problems typically arising from iterative linearization methods used to solve nonlinear PDEs. Due to the object oriented programming paradigm, the code can be used easily and is readily extensible. We explain the basic principles of our code and give numerical experiments that underline its flexibility as well as its efficiency.

Suggested Citation

  • Innerberger, Michael & Praetorius, Dirk, 2023. "MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322007998
    DOI: 10.1016/j.amc.2022.127731
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    References listed on IDEAS

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    1. Dudzinski, Michael & Rozgic̀, Marco & Stiemer, Marcus, 2018. "oFEM: An object oriented finite element package for Matlab," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 117-140.
    2. Čermák, M. & Sysala, S. & Valdman, J., 2019. "Efficient and flexible MATLAB implementation of 2D and 3D elastoplastic problems," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 595-614.
    3. Moskovka, Alexej & Valdman, Jan, 2022. "Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements," Applied Mathematics and Computation, Elsevier, vol. 424(C).
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