Nonsmooth Area On Elliptic Partial Differential Equation Of Numerical Solution

From begin of the Finite Difference Method to present common the Bound-ary Element Method and the Meshless Method, it has been around a long time for studying the numerical solution of partial differential equations. Especially, the Boundary Element Method for solving elliptic partial differential equations of the numerical solution, it has made many is simple, effective conclusions and methods.This paper mainly considers the numerical solution for the Laplace equation and Helmholtz equation on the domain corner. For Robin boundary value prob-lems of the Laplace equation and, the Helmholtz equation of Driblet boundary value problems, Impedance boundary value problem. We use potentials theory and modified jump relations will the corresponding boundary value problem is transformed into the second kind of boundary integral equation. In discrete, to reduce corner bring about the numerical error, we use graded meshes trans-formation of the boundary. Then, we used the Nystrom method to solve the boundary integral equation of the corresponding linear equations. Given all kinds of boundary value conditions of the numerical example, the results show that, for the non-smooth boundary Elliptic partial differential equation, using this method is feasible.This article mainly:1, Give the smooth boundary the jump relationship, and extended to the non-smooth boundary the corresponding jump relationship.2, Give this to use several numerical integral formulas derivation.3, Give the solving method for the Robin boundary value problem of the Laplace equation on the domain corner and numerical example. 4, Give the solving algorithm for the Dirichlet boundary conditions and Impedance boundary conditions the Helmholtz equation on the domain corner and numerical example.