Finite element approximation of the parabolic fractional obstacle problem

Enrique Otarola; Abner J. Salgado

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arXiv · 1507.01985

Finite element approximation of the parabolic fractional obstacle problem

Enrique Otarola·Abner J. Salgado

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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

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Enrique Otarola, Abner J. Salgado. 2015-07-07. Finite element approximation of the parabolic fractional obstacle problem. https://arxiv.org/abs/1507.01985

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