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数学学院、所系列学术报告(789场):孟祥云 北京计算科学研究中心

发表于: 2018-06-20 09:41  点击:

Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions

 

报告人:孟祥云 北京计算科学研究中心

 

时间:2018年6月21日(周四) 上午10:00-11:00

 

地点:数学楼627

 

Abstract:We consider the singularly perturbed fourth-order boundary value problem on the unit square, with Dirichlet boundary conditions. The problem is solved numerically using Adini finite elements -- a simple nonconforming finite element method for this problem. Under reasonable assumptions on the structure of the boundary layers that appear in the solution, a family of suitable Shishkin meshes is constructed and convergence of the method is proved in a ‘broken’ version of the Sobolev norm. This convergence is of a higher order than has been attained by nonconforming elements in previous work on this problem.