AN hp-FEM FOR SINGULARLY PERTURBED TRANSMISSION PROBLEMS

doi:10.4208/jcm.1607-m2014-0187

Journal of Computational Mathematics ›› 2017, Vol. 35 ›› Issue (2): 152-168.DOI: 10.4208/jcm.1607-m2014-0187

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AN hp-FEM FOR SINGULARLY PERTURBED TRANSMISSION PROBLEMS

Serge Nicaise¹, Christos Xenophontos²

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

Received:2015-01-13 Revised:2016-07-25 Online:2017-03-15 Published:2017-03-15
Contact: Christos Xenophontos

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Serge Nicaise, Christos Xenophontos. AN hp-FEM FOR SINGULARLY PERTURBED TRANSMISSION PROBLEMS[J]. Journal of Computational Mathematics, 2017, 35(2): 152-168.

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 presented.

Key words: Singularly perturbed transmission problem, Boundary layers, Interface layers, hp-FEM, Balanced norm, Exponential convergence

CLC Number:

65N30

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AN hp-FEM FOR SINGULARLY PERTURBED TRANSMISSION PROBLEMS

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