Weighted-norm first-order system least squares (FOSLS) for problems with corner singularities

E. Lee, T. A. Manteuffel, C. R. Westphal

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

A weighted-norm least-squares method is considered for the numerical approximation of solutions that have singularities at the boundary. While many methods suffer from a global loss of accuracy due to boundary singularities, the least-squares method can be particularly sensitive to a loss of regularity. The method we describe here requires only a rough lower bound on the power of the singularity and can be applied to a wide range of elliptic equations. Optimal order discretization accuracy is achieved in weighted H 1, and functional norms and L 2 accuracy are retained for boundary value problems with a dominant div/curl operator. Our analysis, including interpolation bounds and several Poincaré-type inequalities, are carried out in appropriately weighted Sobolev spaces. Numerical results confirm the error bounds predicted in the analysis.

Original languageEnglish
Pages (from-to)1974-1996
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume44
Issue number5
DOIs
Publication statusPublished - 2006

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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