Now showing items 1-10 of 11
Gravitational Forces in Dual-Porosity Models of Single Phase Flow
A dual porosity model is derived by the normal theory of homogenization. The model properly incorporates gravity in that it respects the equilibrium states of the medium.
Mixed Finite Element Methods as Finite Difference Methods for Solving Elliptic Equations on Triangular Elements
Several procedures of mixed finite element type for solving elliptic partial differential equations are presented. The efficient implementation of these approaches using the lowest-order Raviart-Thomas approximating spaces ...
A New Formulation of Mixed Finite Element Methods for Second Order Elliptic Problems
In this paper we show that mixed finite element methods for a fairly general second order elliptic problem with variable coefficients can be given a nonmixed formulation. We define an approximation method by incorporating ...
Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Finite Differences
We develop the theory of an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient. The mixed method is expanded in the sense that three variables are explicitly ...
Simulation of Flow in Root-Soil Systems
In this paper we develop a mathematical model of a root-soil system, and also accurate and efficient finite element and finite difference algorithms for approximating this model. The goal of our work is to develop an ...
The Existence of Weak Solutions to Single Porosity and Simple Dual-Porosity Models of Two-Phase Incompressible Flow
It is shown that there exists a weak solution to a degenerate and singular elliptic-parabolic partial integro-differential system of equations. These equations model two-phase incompressible flow of immiscible fluids in ...
Simplified Dual-Porosity Model for Two-Phase Flow
A model for two-phase, incompressible, immiscible fluid flow in a highly fractured porous medium is derived as a simplification of a much more detailed dual-porosity model. This simplified model has a nonlinear matrix-fracture ...
Numerical Methods for the Simulation of Flow in Root-Soil Systems
We consider the numerical properties of approximation schemes for a model that simulates water transport in root-soil systems. The model given in this paper is a reformulation of a previously proposed model now defined ...
A Characteristics-Mixed Finite Element Method for Advection Dominated Transport Problems
We define a new finite element method, called the characteristics-mixed method, for approximating the solution to an advection dominated transport problem. The method is based on a space-time variational form of the ...