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.