Finite element approximation of a singular elliptic problem with discontinuous coefficients

Nada El Berdan (1) , Ahmad Makki (2) , Morgan Pierre (2)

1 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]
2 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

We propose a finite element discretization of a singular elliptic problem with discontinuous coefficients. We use a "regularize then discretize" approach. We show that our method converges in 1, 2 and 3 space dimensions. We also perform numerical simulations in two space dimensions with FreeFem++, using an adaptive mesh strategy to deal with the singularity. The simulations confirm the validity of our approach.

Mots clés: finite element method; singular elliptic problem; monotone operator; adaptive mesh refinement Mathematics Subject Classification: 65N30; 35J70; 47H05; 65N50

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

Nada El Berdan, Ahmad Makki, Morgan Pierre. Finite element approximation of a singular elliptic problem with discontinuous coefficients. 2020. ⟨hal-02971693⟩