An hp Finite Element Method for singularly perturbed transmission problems in smooth domains
Analysis of PDEs
2011-04-06 v1
Abstract
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high and interface layers along the interface. Utilizing existing and newly derived regularity results for the exact solution, we design a robust finite element method for its approximation. Under the assumption of analytic input data, we show that the method converges at an e{xponential} rate, provided the mesh and polynomial degree distribution are chosen appropriately. Numerical results illustrating our theoretical findings are also included.
Cite
@article{arxiv.1104.0766,
title = {An hp Finite Element Method for singularly perturbed transmission problems in smooth domains},
author = {Serge Nicaise and Xenophontos Christos},
journal= {arXiv preprint arXiv:1104.0766},
year = {2011}
}