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Full-Text Articles in Applied Mathematics
A Posteriori Estimates Using Auxiliary Subspace Techniques, Harri Hakula, Michael Neilan, Jeffrey S. Ovall
A Posteriori Estimates Using Auxiliary Subspace Techniques, Harri Hakula, Michael Neilan, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
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 …