phi-FEM for the heat equation: optimal convergence on unfitted meshes in space - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Comptes Rendus. Mathématique Year : 2023

phi-FEM for the heat equation: optimal convergence on unfitted meshes in space

Abstract

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 phi-FEM paradigm, which supposes that the domain is given by a level-set function. In this paper, we prove a priori error estimates in L 2 (H 1) and L ∞ (L 2) norms for an implicit Euler discretization in time. We give numerical illustrations to highlight the performances of phi-FEM, which combines optimal convergence accuracy, easy implementation process and fastness.
Fichier principal
Vignette du fichier
heat_cras_hal.pdf (1.59 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03685445 , version 1 (02-06-2022)
hal-03685445 , version 2 (22-03-2023)

Identifiers

Cite

Michel Duprez, Vanessa Lleras, Alexei Lozinski, Killian Vuillemot. phi-FEM for the heat equation: optimal convergence on unfitted meshes in space. Comptes Rendus. Mathématique, 2023, 361 (G11), pp.1699-1710. ⟨10.5802/crmath.497⟩. ⟨hal-03685445v2⟩
168 View
174 Download

Altmetric

Share

Gmail Facebook X LinkedIn More