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. Araya, Rodolfo; Aguayo, Jorge; Muñoz, Santiago: An adaptive stabilized method for advection-diffusion-reaction equation (2020)
  2. Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.: Optimization of a multiphysics problem in semiconductor laser design (2019)
  3. Walloth, Mirjam: A reliable, efficient and localized error estimator for a discontinuous Galerkin method for the Signorini problem (2019)
  4. Alouges, François; Aussal, Matthieu: FEM and BEM simulations with the Gypsilab framework (2018)
  5. Dudzinski, Michael; Rozgi\`{c}, Marco; Stiemer, Marcus: (o) FEM: an object oriented finite element package for Matlab (2018)
  6. Li, Guanglian; Xu, Yifeng: A convergent adaptive finite element method for cathodic protection (2017)
  7. Rokoš, O.; Peerlings, R. H. J.; Zeman, J.: Extended variational quasicontinuum methodology for lattice networks with damage and crack propagation (2017)
  8. Russell, Stephen; Madden, Niall: An introduction to the analysis and implementation of sparse grid finite element methods (2017)
  9. Cuvelier, François; Japhet, Caroline; Scarella, Gilles: An efficient way to assemble finite element matrices in vector languages (2016)
  10. Nguyen-Xuan, H.; Wu, C. T.; Liu, G. R.: An adaptive selective ES-FEM for plastic collapse analysis (2016)
  11. Anjam, I.; Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements (2015)
  12. Fu, Zhixing; Gatica, Luis F.; Sayas, Francisco-javier: Algorithm 949: MATLAB tools for HDG in three dimensions (2015)
  13. Nguyen-Xuan, H.; Liu, G. R.: An edge-based finite element method (ES-FEM) with adaptive scaled-bubble functions for plane strain limit analysis (2015)
  14. Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk: HILBERT -- a MATLAB implementation of adaptive 2D-BEM. (\underline\textH)ilbert (\underline\textI)s a (\underline\textL)ovely (\underline\textB)oundary (\underline\textE)lement (\underline\textR)esearch (\underline\textT)ool (2014)
  15. Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk: Mixed conforming elements for the large-body limit in micromagnetics (2014)
  16. Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun: A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes (2014)
  17. Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.: Axioms of adaptivity (2014)
  18. Papež, J.; Liesen, J.; Strakoš, Z.: Distribution of the discretization and algebraic error in numerical solution of partial differential equations (2014)
  19. Nguyen-Xuan, H.; Liu, G. R.; Bordas, S.; Natarajan, S.; Rabczuk, T.: An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order (2013)
  20. Rahman, Talal; Valdman, Jan: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements (2013)

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