Efficient implementation of adaptive P1-FEM in Matlab. We provide a Matlab package p1afem for an adaptive P1-finite element method (AFEM). This includes functions for the assembly of the data, different error estimators, and an indicator-based adaptive meshrefining algorithm. Throughout, the focus is on an efficient realization by use of Matlab built-in functions and vectorization. Numerical experiments underline the efficiency of the code which is observed to be of almost linear complexity with respect to the runtime. Although the scope of this paper is on AFEM, the general ideas can be understood as a guideline for writing efficient Matlab code

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  1. Avijit, D.; Natesan, S.: An efficient DWR-type a posteriori error bound of SDFEM for singularly perturbed convection-diffusion PDEs (2022)
  2. Bespalov, Alex; Rocchi, Leonardo; Silvester, David: T-IFISS: a toolbox for adaptive FEM computation (2021)
  3. Chen, Lin; Li, Bin; de Borst, René: The use of Powell-Sabin B-splines in a higher-order phase-field model for crack kinking (2021)
  4. Feischl, Michael; Scaglioni, Andrea: Convergence of adaptive stochastic collocation with finite elements (2021)
  5. Funken, Stefan A.; Schmidt, Anja: A coarsening algorithm on adaptive red-green-blue refined meshes (2021)
  6. Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P.: Energy contraction and optimal convergence of adaptive iterative linearized finite element methods (2021)
  7. Innerberger, Michael; Praetorius, Dirk: Instance-optimal goal-oriented adaptivity (2021)
  8. Ioan, Daniel; Ciuprina, Gabriela; Schilders, Wilhelmus H. A.: Complexity reduction of electromagnetic systems (2021)
  9. Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel: Functional a posteriori error estimates for boundary element methods (2021)
  10. Araya, Rodolfo; Aguayo, Jorge; Muñoz, Santiago: An adaptive stabilized method for advection-diffusion-reaction equation (2020)
  11. Cavoretto, Roberto; De Rossi, Alessandra: A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs (2020)
  12. Celiker, Emine; Lin, Ping: An efficient finite element method with exponential mesh refinement for the solution of the Allen-Cahn equation in non-convex polygons (2020)
  13. Funken, Stefan A.; Schmidt, Anja: Adaptive mesh refinement in 2D -- an efficient implementation in \textscMatlab (2020)
  14. Heid, Pascal; Wihler, Thomas P.: Adaptive iterative linearization Galerkin methods for nonlinear problems (2020)
  15. Karkulik, Michael: A finite element method for elliptic Dirichlet boundary control problems (2020)
  16. Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.: Optimization of a multiphysics problem in semiconductor laser design (2019)
  17. Funken, Stefan A.; Schmidt, Anja: \textttameshref: a Matlab-toolbox for adaptive mesh refinement in two dimensions (2019)
  18. Walloth, Mirjam: A reliable, efficient and localized error estimator for a discontinuous Galerkin method for the Signorini problem (2019)
  19. Alouges, François; Aussal, Matthieu: FEM and BEM simulations with the Gypsilab framework (2018)
  20. Dudzinski, Michael; Rozgić, Marco; Stiemer, Marcus: (o) FEM: an object oriented finite element package for Matlab (2018)

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