A Posteriori Estimates Using Auxiliary Subspace Techniques

Research output: Scientific - peer-reviewArticle

Details

Original languageEnglish
Pages (from-to)97-127
Number of pages31
JournalJOURNAL OF SCIENTIFIC COMPUTING
Volume72
Issue number1
StatePublished - 1 Jul 2017
MoE publication typeA1 Journal article-refereed

Researchers

Research units

  • University of Pittsburgh
  • Portland State University

Abstract

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd(d≥2) are considered. In this approach, the solution of a global problem is utilized as the error estimator. As the continuity and coercivity of the problem trivially leads to an efficiency bound, the main focus of this paper is to derive an analogous effectivity bound and to determine the computational complexity of the auxiliary approximation problem. With a carefully chosen auxiliary subspace, we prove that the error is bounded above by the error estimate up to oscillation terms. In addition, we show that the stiffness matrix of the auxiliary problem is spectrally equivalent to its diagonal. Several numerical experiments are presented verifying the theoretical results.

    Research areas

  • A posteriori error estimation, Finite element methods, High-order methods

ID: 13637111