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Main Title: Supraconvergence and Supercloseness of a Discretisation for Elliptic Third-kind Boundary-value Problems on Polygonal Domains
Author(s): Emmrich, Etienne
Type: Article
Language Code: en
Abstract: The third-kind boundary-value problem for a second-order elliptic equation on a polygonal domain with variable coefficients, mixed derivatives, and first-order terms is approximated by a linear finite element method with first-order accurate quadrature. The corresponding bilinear form does not need to be strongly positive. The discretisation is equivalent to a finite difference scheme. Although the discretisation is in general only first-order consistent, supraconvergence, i.e., convergence of higher order, is shown to take place even on nonuniform grids. If neither oblique boundary sections nor mixed derivatives occur, then the optimal order s is achieved. The supraconvergence result is equivalent to the supercloseness of the gradient.
Issue Date: 2007
Date Available: 10-Oct-2018
DDC Class: 510 Mathematik
Subject(s): elliptic PDE
fully discrete FEM
nonuniform grid
supercloseness of gradient
Journal Title: Computational methods in applied mathematics
Publisher: De Gruyter
Publisher Place: Berlin
Volume: 7
Issue: 2
Publisher DOI: 10.2478/cmam-2007-0008
Page Start: 135
Page End: 162
EISSN: 1609-9389
ISSN: 1609-4840
Appears in Collections:Inst. Mathematik » Publications

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