AFEM@matlab is a MATLAB package of adaptive finite element methods (AFEMs) for stationary and evolution partial differential equations in two spatial dimensions. It contains robust, efficient, and easy-following codes for the main building blocks of AFEMs. This will benefit not only the education of the methods but also future research and algorithmic development. Our package can be useful for education, communication, and research. More precisely, it will (1) speed up program development; (2) facilitate comparisons of ideas and results; (3) improve academic publications. We summarize and emphasis the main features of our package as the following: It includes newest development of AFEMs. It is concise and easy to follow. It can be easily modified for other problems and languages.

References in zbMATH (referenced in 33 articles )

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  1. Dong, Guozhi; Guo, Hailong: Parametric polynomial preserving recovery on manifolds (2020)
  2. Funken, Stefan A.; Schmidt, Anja: Adaptive mesh refinement in 2D -- an efficient implementation in \textscMatlab (2020)
  3. Guo, Hailong: Surface Crouzeix-Raviart element for the Laplace-Beltrami equation (2020)
  4. Funken, Stefan A.; Schmidt, Anja: \textttameshref: a Matlab-toolbox for adaptive mesh refinement in two dimensions (2019)
  5. Soares, D.; Godinho, L.: Adaptive analysis of acoustic-elastodynamic interacting models considering frequency domain MFS-FEM coupled formulations (2019)
  6. Joshi, Vaibhav; Jaiman, Rajeev K.: An adaptive variational procedure for the conservative and positivity preserving Allen-Cahn phase-field model (2018)
  7. Nguyen-Thanh, Vien Minh; Zhuang, Xiaoying; Nguyen-Xuan, Hung; Rabczuk, Timon; Wriggers, Peter: A virtual element method for 2D linear elastic fracture analysis (2018)
  8. Abdulle, Assyr; Budáč, Ondrej: A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media (2017)
  9. Abdulle, Assyr; Budáč, Ondrej; Imboden, Antoine: A three-scale offline-online numerical method for fluid flow in porous media (2017)
  10. Apel, Thomas; Nicaise, Serge; Pfefferer, Johannes: Adapted numerical methods for the Poisson equation with (L^2) boundary data in nonconvex domains (2017)
  11. Godinho, L.; Soares, Delfim jun.: Numerical simulation of soil-structure elastodynamic interaction using iterative-adaptive BEM-FEM coupled strategies (2017)
  12. Abdulle, Assyr; Budáč, Ondrej: A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media (2016)
  13. Soares, Delfim; Godinho, L.: Heat conduction analysis by adaptive iterative BEM-FEM coupling procedures (2016)
  14. 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)
  15. Zeng, Yuping; Chen, Jinru; Wang, Feng: A posteriori error estimates of a weakly over-penalized symmetric interior penalty method for elliptic eigenvalue problems (2015)
  16. Abdulle, Assyr; Bai, Yun: Adaptive reduced basis finite element heterogeneous multiscale method (2013)
  17. Hintermüller, M.; Hinze, M.; Kahle, C.: An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system (2013)
  18. Le, Canh V.: A stabilized discrete shear gap finite element for adaptive limit analysis of Mindlin-Reissner plates (2013)
  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. Apel, Thomas; Flaig, Thomas G.: Crank--Nicolson schemes for optimal control problems with evolution equations (2012)

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