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. Li, Guanglian; Xu, Yifeng: A convergent adaptive finite element method for cathodic protection (2017)
  2. Russell, Stephen; Madden, Niall: An introduction to the analysis and implementation of sparse grid finite element methods (2017)
  3. Cuvelier, François; Japhet, Caroline; Scarella, Gilles: An efficient way to assemble finite element matrices in vector languages (2016)
  4. Nguyen-Xuan, H.; Wu, C. T.; Liu, G. R.: An adaptive selective ES-FEM for plastic collapse analysis (2016)
  5. Fu, Zhixing; Gatica, Luis F.; Sayas, Francisco-javier: Algorithm 949: MATLAB tools for HDG in three dimensions (2015)
  6. 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. $\underline \text H$ilbert $\underline \text I$s a $\underline \text L$ovely $\underline \text B$oundary $\underline \text E$lement $\underline \text R$esearch $\underline \text T$ool (2014)
  7. Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk: Mixed conforming elements for the large-body limit in micromagnetics (2014)
  8. Carstensen, Carsten; Gallistl, Dietmar; Hu, Jun: A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes (2014)
  9. Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.: Axioms of adaptivity (2014)
  10. Papež, J.; Liesen, J.; Strakoš, Z.: Distribution of the discretization and algebraic error in numerical solution of partial differential equations (2014)
  11. 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)
  12. Rahman, Talal; Valdman, Jan: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements (2013)
  13. Carstensen, Carsten; Gedicke, Joscha: An adaptive finite element eigenvalue solver of asymptotic quasi-optimal computational complexity (2012)
  14. Cockburn, Bernardo; Zhang, Wujun: A posteriori error estimates for HDG methods (2012)
  15. Funken, Stefan; Praetorius, Dirk; Wissgott, Philipp: Efficient implementation of adaptive P1-FEM in Matlab (2011)
  16. Nguyen-Thoi, T.; Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Tran, C.: Adaptive analysis using the node-based smoothed finite element method (NS-FEM) (2011)