An Effective Indirect Trefftz Method for Solving Poisson Equation in 2D

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Poisson equation indirect Trefftz method Galerkin method boundary problem numerical method
• 年，卷（期）: 2017,（1）
• 页码范围: 1-10
• 页数: 10页
• 分类号: O175.25
• 语种: 英文
• DOI: 10.4208/jpde.v30.n1.1

摘要

In the solution domain,the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method,and the particular solution of the polynomial can be determined easily.Then,the solution of the Poisson equation is approximated by superposition of the particular solution and the Tcomplete functions related to the Laplace equation.Unknown parameters are determined by Galerkin method,so that the approximate solution is to satisfy the boundary conditions.Comparison with analogous results of others numerical method,the two calculating examples of the paper indicate that the accuracy of the method is very high,which also has a very fast convergence rate.