Theoretical and Numerical Analysis of a Class of Nonlinear Elliptic Equations

Nour Eddine Alaa (1) , Jean Rodolphe Roche (1, 2)

1 CALVI - Scientific computation and visualization
2 IECN - Institut Élie Cartan de Nancy

In this paper we show the existence of weak solutions for a nonlinear elliptic equations with arbitrary growth of the non linearity and data measure. A numerical algorithm to compute a numerical approximation of the weak solution is described and analyzed. In a first step a super-solution is computed using a domain decomposition method. Numerical examples are presented and commented.

Mots clés: Domain decomposition; Nonlinear elliptic PDE

Domaines: Analyse numérique [math.NA]

Nour Eddine Alaa, Jean Rodolphe Roche. Theoretical and Numerical Analysis of a Class of Nonlinear Elliptic Equations. Mediterranean Journal of Mathematics, 2005, 2, pp.327-344. ⟨10.1007/s00009-005-0048-4⟩. ⟨hal-00095236⟩