This thesis is dedicated to
致谢
ABSTRACT
CHAPTER 1: THEORETIC AL PRELIMINARIES
§ 1.1 Sobolev spaces
§1.2Computational meshes and volume construction
§ 1.3 Finite element space and dual volume element space
§ 1.4 Green function and its properties
CHAPTER 2: FINITE VOLUME ELEMENT METHOD FOR ADVECTION-DIFFUSION ELLIPTIC EQUATIONS
§ 2.1 Formulation of the problem
§ 2.2 Finite volume element method
§ 2.3 Error estimates
CHAPTER 3: FINITE VOLUME ELEMENT METHOD FOR PARABOLIC EQUATIONS
§ 3.1 Formulation of the problem
§ 3.2 Semi-discrete finite volume element scheme
§ 3.3 Error estimates of the semi-discrete scheme
§ 3.4 Error estimates of the Crank-Nicolson scheme
CHAPTER 4: FINITE VOLUME ELEMENT METHOD FOR 1-DIMENSIONAL PSEUDO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS
§4.1 Introduction
§ 4.2 Finite volume element
§ 4.3 Error Estimates
CHAPTER 5: FINITE VOLUME ELEMENT METHOD FOR INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEM IN POROUS MEDIA
§ 5.1 Mathematical formulation of the problem
§ 5.2 Finite volume element method
§ 5.3 convergence analysis
CHAPTER 6: A MIXED METHOD FOR THE POLLUTION OF THE GROUND WATER IN DOUBLE POROUS MEDIA
§ 6.1 Problem formulation
§ 6.2 The approximation procedure
§ 6.3 Convergence analysis
CHAPTER 7: FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS
§ 7.1 Formulation of the problem
§ 7.2 Semi-discrete finite element scheme
§ 7.3 Error estimates of the semi-discrete problem
§ 7.4 Error estimates of the fully discrete scheme
BIBLIOGRAPHY
APPENDIX
