Finite element approximation of the parabolic fractional obstacle problem
Numerical Analysis
2015-07-09 v1
Abstract
We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite cylinder, which recasts our problem as a quasi-stationary elliptic variational inequality with a dynamic boundary condition. The rapid decay of the solution suggests a truncation that is suitable for numerical approximation. We discretize the truncation with a backward Euler scheme in time and, for space, we use first-degree tensor product finite elements. We present an error analysis based on different smoothness assumptions
Cite
@article{arxiv.1507.01985,
title = {Finite element approximation of the parabolic fractional obstacle problem},
author = {Enrique Otarola and Abner J. Salgado},
journal= {arXiv preprint arXiv:1507.01985},
year = {2015}
}