Thumbnail
Access Restriction
Open

Author Costabel, Martin ♦ Dauge, Monique ♦ Nicaise, Serge
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-02-08
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Analysis of PDEs ♦ Mathematics - Numerical Analysis ♦ math
Abstract We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing exponential convergence for hp finite element methods in polyhedra. We first give a simple proof of the known weighted analytic regularity in a polygon, relying on a new formulation of elliptic a priori estimates in smooth domains with analytic control of derivatives. The technique is based on dyadic partitions near the corners. This technique can successfully be extended to polyhedra, providing isotropic analytic regularity. This is not optimal, because it does not take advantage of the full regularity along the edges. We combine it with a nested open set technique to obtain the desired three-dimensional anisotropic analytic regularity result. Our proofs are global and do not require the analysis of singular functions.
Educational Use Research
Learning Resource Type Article
Page Count 54


Open content in new tab

   Open content in new tab