Error Analysis for a Galerkin Finite Element Method Applied to a Coupled Nonlinear Degenerate System of Advection-diffusion Equations

Autor:	Koffi B. Fadimba
Rok vydání:	2006
Předmět:	Computational Mathematics Numerical Analysis Nonlinear system Discretization Discontinuous Galerkin method Applied Mathematics Applied mathematics Mixed finite element method Uniqueness Galerkin method Finite element method Mathematics Extended finite element method
Zdroj:	Computational Methods in Applied Mathematics. 6:3-30
ISSN:	1609-9389 1609-4840
DOI:	10.2478/cmam-2006-0001
Popis:	We consider a standard Galerkin Method applied to both the pressure equation and the saturation equation of a coupled nonlinear system of degenerate advection-diffusion equations modeling a two-phase immiscible flow through porous media. After regularizing the problem and establishing some regularity results, we derive error estimates for a semi-discretized Galerkin Method. A decoupled nonlinear scheme is then proposed for a fully discretized (backward in time) Galerkin Method, and error estimates are derived for that method. We also prove the existence and uniqueness for the nonlinear operator intervening in the backward time discretization.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fed0810e2414a3645ea8cdd5483833b5 https://doi.org/10.2478/cmam-2006-0001 Zobrazit plný text záznamu