Regularity and a priori error analysis of a Ventcel problem in polyhedral domains

Serge Nicaise, Hengguang Li, Anna Mazzucato

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5 Scopus citations

Abstract

We consider the regularity of a mixed boundary value problem for the Laplace operator on a polyhedral domain, where Ventcel boundary conditions are imposed on one face of the polyhedron and Dirichlet boundary conditions are imposed on the complement of that face in the boundary. We establish improved regularity estimates for the trace of the variational solution on the Ventcel face and use them to derive a decomposition of the solution into a regular and a singular part that belongs to suitable weighted Sobolev spaces. This decomposition, in turn, via interpolation estimates both in the interior as well as on the Ventcel face, allows us to perform an a priori error analysis for the finite element approximation of the solution on anisotropic graded meshes. Numerical tests support the theoretical analysis.

Original languageEnglish (US)
Pages (from-to)1625-1636
Number of pages12
JournalMathematical Methods in the Applied Sciences
Volume40
Issue number5
DOIs
StatePublished - Mar 30 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

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