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Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Sep 13, 2015;373 (2050):

Convergence rates for the classical, thin and fractional elliptic obstacle problems.

Ricardo H Nochetto, Enrique Otárola, Abner J Salgado
Author Information
  1. Ricardo H Nochetto: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA rhn@math.umd.edu.
  2. Enrique Otárola: Department of Mathematics, University of Maryland, College Park, MD 20742, USA Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA.
  3. Abner J Salgado: Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA.
PMID: 26261371 DOI: 10.1098/rsta.2014.0449

Abstract

We review the finite-element approximation of the classical obstacle problem in energy and max-norms and derive error estimates for both the solution and the free boundary. On the basis of recent regularity results, we present an optimal error analysis for the thin obstacle problem. Finally, we discuss the localization of the obstacle problem for the fractional Laplacian and prove quasi-optimal convergence rates.

Keywords

anisotropic elements finite elements fractional diffusion free boundaries obstacle problem thin obstacles
Journal Article Research Support, U.S. Gov't, Non-P.H.S.
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