Convergence rates for the classical, thin and fractional elliptic obstacle problems.
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.
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA rhn@math.umd.edu.
Ricardo H
RH
Nochetto
Department of Mathematics, University of Maryland, College Park, MD 20742, USA Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA.
Enrique
E
Otárola
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA.
Abner J
AJ
Salgado
anisotropic elements; finite elements; fractional diffusion; free boundaries; obstacle problem; thin obstacles