Higher-order finite element methods for elliptic problems with interfaces

Johnny Guzmán, Manuel A. Sánchez, Marcus Sarkis

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.

Original languageEnglish (US)
Pages (from-to)1561-1583
Number of pages23
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume50
Issue number5
DOIs
StatePublished - Sep 1 2016

Bibliographical note

Publisher Copyright:
© EDP Sciences, SMAI 2016.

Keywords

  • Finite elements
  • Interface problems
  • Pointwise estimates

Fingerprint

Dive into the research topics of 'Higher-order finite element methods for elliptic problems with interfaces'. Together they form a unique fingerprint.

Cite this