Hierarchical error estimates for the energy functional in obstacle problems
Zou Q, Veeser A, Kornhuber R, Graeser C (2011)
Publication Type: Journal article
Publication year: 2011
Journal
Book Volume: 117
Pages Range: 653-677
Journal Issue: 4
DOI: 10.1007/s00211-011-0364-5
Abstract
We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations. © 2011 Springer-Verlag.
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APA:
Zou, Q., Veeser, A., Kornhuber, R., & Graeser, C. (2011). Hierarchical error estimates for the energy functional in obstacle problems. Numerische Mathematik, 117(4), 653-677. https://dx.doi.org/10.1007/s00211-011-0364-5
MLA:
Zou, Qingsong, et al. "Hierarchical error estimates for the energy functional in obstacle problems." Numerische Mathematik 117.4 (2011): 653-677.
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