MIXED FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS AND ITS ALTERNATING-DIRECTION ITERATIVE SCHEME

In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.

CHARACTERISTIC FINITE DIFFERENCE ALTERNATING-DIRECTION METHOD ANDANALYSIS FOR NUMERICAL RESERVOIR SIMULATION

Petroleum science has made remarkable progress in organic geochemistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model call be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the characteristic of large-scal science-engineering computalion. puts forward a kind of characteristic finite difference alternating-direction scheme. Optimal order estimates in L-2 norm are derived for the error in the approximate solutions.

ALTERNATING-DIRECTION MULTISTEP PRECONDITIONED ITERATIVE METHODS FOR SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.

THE CHARACTERISTIC FINITE ELEMENT ALTERNATING-DIRECTION METHOD AND ANALYSIS FOR THREE-DIMENSIONAL NUMERICAL RESERVOIR SIMULATION

Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L^2 norm for the error in the approximate assumption.

The Alternating-Direction Schemes and Numerical Analysis for the Three-dimensional Seawater Intrusion Simulation

Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristic of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H1 norm are derived for the error in the approximate solution.

Theoretical Proof of Unconditional Stability of the 3-D ADI-FDTD Method

In order to eliminate Courant-Friedrich-Levy(CFL) condition restraint and improvecomputational efficiency,a new finite-difference time-domain(FDTD)method based on the alternating-direction implicit(ADI) technique is introduced recently.In this paper,a theoretical proof of the stabilityof the three-dimensional(3-D)ADI-FDTD method is presented.It is shown that the 3-D ADI-FDTDmethod is unconditionally stable and free from the CFL condition restraint.

AN A.D.I.GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION

An A. D. I. Galerkin scheme for three-dimensional nonlinear parabolic integro-differen-tial equation is studied. By using alternating-direction, the three-dimensional problem is reduced to a family of single space variable problems, the calculation is simplified; by using a local approxima-tion of the coefficients based on patches of finite elements, the coefficient matrix is updated at each time step; by using Ritz-Volterra projection, integration by part and other techniques, the influence coming from the integral term is treated; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity is treated. For both Galerkin and A. D. I. Galerkin schemes the con-vergence properties are rigorously demonstrated, the optimal H^1-norm and L^2-norm estimates are obtained.