A NXFEM approximation for a nonlinear system of PDEs

A. Blouza (1) , A-T Dinh (2) , L El Alaoui (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LAGA - Laboratoire Analyse, Géométrie et Applications

Under the motivation of modeling a biofilm model, we introduce a system of semilinear elliptic interface problem. We also propose a technique of decoupling a semilinear problem and apply the Nistche-Extended Finite Element method to prove the existence and uniqueness of solutions and their convergent properties.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

A. Blouza, A-T Dinh, L El Alaoui. A NXFEM approximation for a nonlinear system of PDEs. 2020. ⟨hal-02537616⟩