A stabilised finite element method for a time-dependent problem solved using a fictitious domain method

Gabriel R Barrenechea , Franz Chouly (1) , Cheherazada Gonzalez

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this work we present and analyse a stabilised finite element method for a fictitious domain formulation of a transient heat equation posed on an irregular domain. First, the problem is reformulated as a variational problem with constraints in a larger, simpler domain. In order to have freedom to choose the spaces for primal variable and Lagrange multiplier, we introduce a stabilising term whose consistency error can be shown to be of optimal order. We show that the fully discrete problem is stable and enjoys optimal convergence under the extra assumption that the initial condition has been chosen appropriately. This requirement is not linked to the stabilised character of the method, as the numerical experiments confirm.

Mots clés: Fictitious domain method; stabilised finite element method; time-dependent problem

Domaines: Analyse numérique [math.NA]

Gabriel R Barrenechea, Franz Chouly, Cheherazada Gonzalez. A stabilised finite element method for a time-dependent problem solved using a fictitious domain method. 2017. ⟨hal-01596106⟩