On the accuracy of finite element approximations to a class of interface problems

Johnny Guzmán, Manuel A. Sánchez, Marcus Sarkis

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We define piecewise linear and continuous finite element methods for a class of interface problems in two dimensions. Correction terms are added to the right-hand side of the natural method to render it second-order accurate. We prove that the method is second-order accurate on general quasiuniform meshes at the nodal points. Finally, we show that the natural method, although non-optimal near the interface, is optimal for points O(√h log(1/h)) away from the interface.

Original languageEnglish (US)
Pages (from-to)2071-2098
Number of pages28
JournalMathematics of Computation
Volume85
Issue number301
DOIs
StatePublished - Jan 1 2016

Keywords

  • Finite elements
  • Interface problems
  • Pointwise estimates

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