AN hp-FEM FOR SINGULARLY PERTURBED TRANSMISSION PROBLEMS  

作　　者：Serge Nicaise Christos Xenophontos 

机构地区：[1]Université de Valenciennes et du Hainaut Cambrésis LAMAV, FR CNRS 2956, Institut des Sciences et Techniques de Valenciennes F-59313 - Valenciennes Cedex 9 France [2]Department of Mathematics and Statistics University of Cyprus, P.O. Box 20537 Nicosia 1678, Cyprus

出　　处：《Journal of Computational Mathematics》2017年第2期152-168,共17页计算数学（英文）

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 measured 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 nresented.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 measured 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 nresented.

关 键 词：Singularly perturbed transmission problem Boundary layers Interface layers hp-FEM Balanced norm Exponential convergence. 

分 类 号：O[理学]