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Article
A Posteriori Estimates Using Auxiliary Subspace Techniques
Mathematics and Statistics Faculty Publications and Presentations
  • Harri Hakula, Aalto University
  • Michael Neilan, University of Pittsburgh,
  • Jeffrey S. Ovall, Portland State University
Document Type
Pre-Print
Publication Date
1-1-2014
Subjects
  • Partial differential equations,
  • Constrained optimization,
  • Numerical analysis,
  • Computational complexity
Disciplines
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.
Description

Copyright 2014 The Author's. This is the author's manuscript subsequently submitted to SINUM.

Persistent Identifier
http://archives.pdx.edu/ds/psu/15910
Citation Information
Hakula, H., Neilan, M., & Ovall, J. (2014). A posteriori estimates using auxiliary subspace techniques. Submitted to SINUM.