The 5-point finite analytic schemes for laplace equation in irregular domains;

Based on measuring rock core in lab and started from Laplace equation of capillary,This thesis presents the method of evaluating reservoir wettability using conventional logging data,which realizes continuous,quick and quantitative evaluation of reservoir wettability accordingly.

It is complicated and hard-controlled for beginner to solve the Laplace equation in the static electricity field.

Based on the solution of the Laplace Equations, a numerical procedure for generation of 2-D orthogonal body-fitted curvilinear coordinate system is developed in which the grid points on the boundary can be arbitrarily determined.

Through solving the Laplace equations about physics co ordinate to transform plane,a numerical method of determining the grid points had been successfully used to generate the orthogonal co ordinate system.

The existence of the solution for a singular p-Laplace equation involving critical Sobolev-Hardy exponent is studied: -div〔(|▽u|p-2▽u)/|x|β 〕=(up*-1)/|x|α+λuq-1,inΩ;u=0,onΩ by using Sobolev—Hardy inequality,Concentration Compactness Principle and the Mountain Pass Geometry.

In this paper a sufficient condition for mixed finite element space of lowest order for Laplacian Equation is derived and a new interpolation operator is constructed.