A Posteriori Estimates Using Auxiliary Subspace Techniques

Harri Hakula, Michael Neilan, Jeffrey S. Ovall*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)97-127
Number of pages31
Issue number1
Publication statusPublished - 1 Jul 2017
MoE publication typeA1 Journal article-refereed


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


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