Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh, not fitting the domain and its real boundary exactly. Our technique follows the -FEM paradigm, which supposes that the domain is given by a level-set function. In this paper, we prove a priori error estimates in and norms for an implicit Euler discretization in time. We give numerical illustrations to highlight the performances of -FEM, which combines optimal convergence accuracy, easy implementation process and fastness.
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Michel Duprez 1; Vanessa Lleras 2; Alexei Lozinski 3; Killian Vuillemot 1, 2
@article{CRMATH_2023__361_G11_1699_0, author = {Michel Duprez and Vanessa Lleras and Alexei Lozinski and Killian Vuillemot}, title = {$\phi ${-FEM} for the heat equation: optimal convergence on unfitted meshes in space}, journal = {Comptes Rendus. Math\'ematique}, pages = {1699--1710}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.497}, language = {en}, }
TY - JOUR AU - Michel Duprez AU - Vanessa Lleras AU - Alexei Lozinski AU - Killian Vuillemot TI - $\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space JO - Comptes Rendus. Mathématique PY - 2023 SP - 1699 EP - 1710 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.497 LA - en ID - CRMATH_2023__361_G11_1699_0 ER -
%0 Journal Article %A Michel Duprez %A Vanessa Lleras %A Alexei Lozinski %A Killian Vuillemot %T $\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space %J Comptes Rendus. Mathématique %D 2023 %P 1699-1710 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.497 %G en %F CRMATH_2023__361_G11_1699_0
Michel Duprez; Vanessa Lleras; Alexei Lozinski; Killian Vuillemot. $\phi $-FEM for the heat equation: optimal convergence on unfitted meshes in space. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1699-1710. doi : 10.5802/crmath.497. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.497/
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