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Matching of asymptotic expansions and multiscale expansion for the rounded corner problem

by S. Tordeux and G. Vial

(Report number 2006-04)

Abstract
In this paper we consider the Laplace Dirichlet equation in a polygonal domain which has been slightly perturbed to the scale $\eps$ near one vertex. We derive and validate an asymptotic expansion of the solution via two different techniques: matched asymptotic expansion and multiscale expansion. We present a simple approach of both methods and compare the obtained expansions.

Keywords:

@Techreport{TV06_353,
  author = {S. Tordeux and G. Vial},
  title = {Matching of asymptotic expansions and multiscale expansion for the rounded corner problem},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2006-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2006/2006-04.pdf },
  year = {2006}
}

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