Theoretical and numerical analysis of a coupled system of second order non-linear differential equations

Nouredine Alaa (1) , Mohamed Iguernane (2, 3) , Jean Rodolphe Roche (2, 3)

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

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented.

Mots clés: reaction-diffusion; decomposition des domaines

Domaines: Analyse numérique [math.NA]

Nouredine Alaa, Mohamed Iguernane, Jean Rodolphe Roche. Theoretical and numerical analysis of a coupled system of second order non-linear differential equations. 2006. ⟨hal-00112829⟩