AN hp-FEM FOR SINGULARLY PERTURBED TRANSMISSION PROBLEMS

• 来源期刊: 计算数学（英文版）
• 关键词: Singularly perturbed transmission problem Boundary layers Interface layers hp-FEM Balanced norm Exponential convergence
• 年，卷（期）: 2017,（2）
• 页码范围: 152-168
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1607-m2014-0187

摘要

We perform the analysis of the hp finite element approximation for the solution to singularly perturbed transmission problems,using Spectral Boundary Layer Meshes.In [12] it was shown that this method yields robust exponential convergence,as the degree p of the approximating polynomials is increased,when the error is measnred in the energy norm associated with the boundary value problem.In the present article we sharpen the result by showing that the hp-Finite Element Method (FEM) on Spectral Boundary Layer Meshes leads to robust exponential convergence in a stronger,more balanced norm.Several numerical results illustrating and extending the theory are also presented.