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. Bespalov, Alex; Rocchi, Leonardo; Silvester, David: T-IFISS: a toolbox for adaptive FEM computation (2021)
  2. Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel: Functional a posteriori error estimates for boundary element methods (2021)
  3. Araya, Rodolfo; Aguayo, Jorge; Muñoz, Santiago: An adaptive stabilized method for advection-diffusion-reaction equation (2020)
  4. Cavoretto, Roberto; De Rossi, Alessandra: A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs (2020)
  5. Funken, Stefan A.; Schmidt, Anja: Adaptive mesh refinement in 2D -- an efficient implementation in \textscMatlab (2020)
  6. Heid, Pascal; Wihler, Thomas P.: Adaptive iterative linearization Galerkin methods for nonlinear problems (2020)
  7. Karkulik, Michael: A finite element method for elliptic Dirichlet boundary control problems (2020)
  8. Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.: Optimization of a multiphysics problem in semiconductor laser design (2019)
  9. Funken, Stefan A.; Schmidt, Anja: \textttameshref: a Matlab-toolbox for adaptive mesh refinement in two dimensions (2019)
  10. Walloth, Mirjam: A reliable, efficient and localized error estimator for a discontinuous Galerkin method for the Signorini problem (2019)
  11. Alouges, François; Aussal, Matthieu: FEM and BEM simulations with the Gypsilab framework (2018)
  12. Dudzinski, Michael; Rozgi\`{c}, Marco; Stiemer, Marcus: (o) FEM: an object oriented finite element package for Matlab (2018)
  13. Li, Guanglian; Xu, Yifeng: A convergent adaptive finite element method for cathodic protection (2017)
  14. Rokoš, O.; Peerlings, R. H. J.; Zeman, J.: Extended variational quasicontinuum methodology for lattice networks with damage and crack propagation (2017)
  15. Russell, Stephen; Madden, Niall: An introduction to the analysis and implementation of sparse grid finite element methods (2017)
  16. Cuvelier, François; Japhet, Caroline; Scarella, Gilles: An efficient way to assemble finite element matrices in vector languages (2016)
  17. Nguyen-Xuan, H.; Wu, C. T.; Liu, G. R.: An adaptive selective ES-FEM for plastic collapse analysis (2016)
  18. Anjam, I.; Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements (2015)
  19. Castillo, María Emilia; Morin, Pedro: On a dissolution-diffusion model. Existence, uniqueness, regularity and simulations (2015)
  20. Frank, Florian; Reuter, Balthasar; Aizinger, Vadym; Knabner, Peter: FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. I: Diffusion operator (2015)

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