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Conforming and discontinuous Galerkin FEM in space for solving parabolic obstacle problem

Gudi, Thirupathi and Majumder, Papri (2019) Conforming and discontinuous Galerkin FEM in space for solving parabolic obstacle problem. In: COMPUTERS & MATHEMATICS WITH APPLICATIONS, 78 (12). pp. 3896-3915.

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Official URL: https://dx.doi.org/10.1016/j.camwa.2019.06.022

Abstract

In this article, we propose and analyze conforming and discontinuous Galerkin (DG) finite element methods for numerical approximation of the solution of the parabolic variational inequality associated with a general obstacle in R-d (d = 2, 3). For fully discrete conforming method, we use globally continuous and piecewise linear finite element space. Whereas for the fully-discrete DG scheme, we employ piecewise linear finite element space for spatial discretization. The time discretization has been done by using the implicit backward Euler method. We present the error analysis for the conforming and the DG fully discrete schemes and derive an error estimate of optimal order (h+ Delta t) in a certain energy norm defined precisely in the article. The analysis is performed without any assumptions on the speed of propagation of the free boundary but only assumes the pragmatic regularity that u(t) is an element of L-2 (0, T; L-2(Omega)). The obstacle constraints are incorporated at the Lagrange nodes of the triangular mesh and the analysis exploits the Lagrange interpolation. We present some numerical experiment to illustrate the performance of the proposed methods.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to PERGAMON-ELSEVIER SCIENCE LTD
Keywords: Finite element; Discontinuous Galerkin method; Parabolic obstacle problem
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 16 Jan 2020 06:58
Last Modified: 16 Jan 2020 06:58
URI: http://eprints.iisc.ac.in/id/eprint/64187

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