Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition

Authors:
Z. Chen;R. E. Ewing
Affiliations:
Department of Mathematics, Box 156, Southern Methodist University, Dallas, Texas 75275-0156 zchen@mail.smu.edu;Institute for Scientific Computation, Texas A&M University, College Station, Texas 77843-3404 ewing@ewing.tamu.edu
Venue:
Journal of Scientific Computing
Year:
2003

Citing 14
Cited 0

Mixed finite elements for second order elliptic problems in three variables

Numerische Mathematik
A preconditioning technique for the efficient solution of problems with local grid refinement

Computer Methods in Applied Mechanics and Engineering
The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow

Nonlinear Analysis: Theory, Methods & Applications
Domain decomposition type iterative techniques for parabolic problems on locally refined grids

SIAM Journal on Numerical Analysis
Approximation of parabolic problems on grids locally refined in time and space

Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Inexact and preconditioned Uzawa algorithms for saddle point problems

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Domain decomposition algorithms for mixed methods for second-order elliptic problems

Mathematics of Computation
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems

SIAM Journal on Numerical Analysis
Adaptive mesh refinement and multilevel iteration for flow in porous media

Journal of Computational Physics
Fully Discrete Finite Element Analysis of Multiphase Flow in Groundwater Hydrology

SIAM Journal on Numerical Analysis
Mathematical analysis for reservoir models

SIAM Journal on Mathematical Analysis
Adaptive Computational Methods for Partial Differential Equations

Adaptive Computational Methods for Partial Differential Equations
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Error Analysis for Characteristics-Based Methods for Degenerate Parabolic Problems

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

This is the fourth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we describe a finite element approximation for this system on locally refined grids. This adaptive approximation is based on a mixed finite element method for the elliptic pressure equation and a Galerkin finite element method for the degenerate parabolic saturation equation. Both discrete stability and sharp a priori error estimates are established for this approximation. Iterative techniques of domain decomposition type for solving it are discussed, and numerical results are presented.