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Error Analysis for a Galerkin Finite Element Method Applied to a Coupled Nonlinear Degenerate System of Advection-diffusion Equations
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Koffi B. Fadimba
Published/Copyright:
January 1, 2006
Abstract
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.
Keywords: porous media; two-phase flow; regularization; error analysis; finite element method; nonlinear partial differential equation; advection-diffusion; coupled system; nonlinear scheme
Received: 2005-10-07
Revised: 2005-12-22
Accepted: 2006-03-01
Published Online: 2006
Published in Print: 2006
© Institute of Mathematics, NAS of Belarus
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- Improved Applications of Relaxation Schemes for Hyperbolic Systems of Conservation Laws and Convection-diffusion Problems
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Keywords for this article
porous media;
two-phase flow;
regularization;
error analysis;
finite element method;
nonlinear partial differential equation;
advection-diffusion;
coupled system;
nonlinear scheme
Articles in the same Issue
- Error Analysis for a Galerkin Finite Element Method Applied to a Coupled Nonlinear Degenerate System of Advection-diffusion Equations
- Stability Criterion of Difference Schemes for the Heat Conduction Equation with Nonlocal Boundary Conditions
- Improved Applications of Relaxation Schemes for Hyperbolic Systems of Conservation Laws and Convection-diffusion Problems
- Bounds of Information Expenses in Constructing Projection Methods for Solving Ill-posed Problems
- Sharp Error Bounds for a Symmetrized Locally 1d Method for Solving the 2d Heat Equation
