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Convergence analysis of finite element method for a parabolic obstacle problem

Gudi, T and Majumder, P (2019) Convergence analysis of finite element method for a parabolic obstacle problem. In: Journal of Computational and Applied Mathematics, 357 . pp. 85-102.


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Official URL: https://dx.doi.org/10.1016/j.cam.2019.02.026


A conforming finite element method is proposed and analyzed for numerical approximation of the solution of a parabolic variational inequality of the obstacle problem. The model problem, which is originally proposed using a general obstacle, is reframed as a model problem with zero obstacle but with non-homogeneous Dirichlet boundary conditions. Subsequently the discrete problem is reframed and the error analysis proving the convergence of the method is performed. The analysis requires a positive preserving interpolation with non-homogeneous Dirichlet boundary condition and a post-processed solution that satisfies the boundary conditions sharply. The results in the article extend the results of (Johnson, SINUM, 1976) for a zero obstacle function to a more general obstacle function.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Science Direct
Keywords: Boundary conditions; Numerical methods; Variational techniques, Conforming finite element method; Convergence analysis; Discrete problems; Numerical approximations; Obstacle problems; Parabolic obstacle problems; Parabolic variational inequality; Variational inequalities, Finite element method
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 09 Apr 2019 05:26
Last Modified: 09 Apr 2019 05:26
URI: http://eprints.iisc.ac.in/id/eprint/62053

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