Mathematical and Numerical Analysis of a Class of Non-linear Elliptic Equations in the Two Dimensional Case

Noureddine Alaa (1) , Jean Rodolphe Roche (2, 3) , A. Cheggour (1)

1 FSTG - Faculte des Sciences et techniques Gueliz
2 CALVI - Scientific computation and visualization
3 IECN - Institut Élie Cartan de Nancy

The aim of this paper is to show the existence and present a numerical analysis of weak solutions for a quasi-linear elliptic problem with Dirichlet boundary conditions in a domain $\Omega$ and data belonging to $L^1(\Omega)$. A numerical algorithm to compute a numerical approximation of the weak solution is described and analyzed. Numerical examples are presented and commented.

Mots clés: Domain decomposition methods; Nonlinear EDP

Domaines: Analyse numérique [math.NA]

Noureddine Alaa, Jean Rodolphe Roche, A. Cheggour. Mathematical and Numerical Analysis of a Class of Non-linear Elliptic Equations in the Two Dimensional Case. Jul 2006, pp.926-936. ⟨hal-00095264⟩