报告题目：An efficient spectral-Galerkin method for elliptic equations in 2D complex geometries
报告时间：2023年3月29日 下午16:00-17:00
报告地点：红瓦楼726室
报告摘要：A polar coordinate transformation is considered, which transforms the complex geometries into a unit disc. Some basic properties of the polar coordinate transformation are given. As applications, we consider the elliptic equation in two-dimensional complex geometries. The existence and uniqueness of the weak solution are proved, the Fourier-Legendre spectral-Galerkin scheme is constructed and the optimal convergence of numerical solutions under $H^1$-norm is analyzed. The proposed method is very effective and easy to implement for problems in 2D complex geometries.
Numerical results are presented to demonstrate the high accuracy of our spectral-Galerkin method.
报告人简介：王中庆，上海理工大学教授，博导。长期从事偏微分方程数值方法的研究工作，在《SIAM J. Numer. Anal.》和《Math. Comp.》等国际学术期刊上发表论文90余篇，主持过多项国家自然科学基金面上项目。