Crouzeix-Raviart Finite Element Approximation for the Parabolic Obstacle Problem

Gudi, T and Majumder, P (2020) Crouzeix-Raviart Finite Element Approximation for the Parabolic Obstacle Problem. In: Computational Methods in Applied Mathematics, 20 (2). pp. 273-292.

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Abstract

We introduce and study a fully discrete nonconforming finite element approximation for a parabolic variational inequality associated with a general obstacle problem. The method comprises of the Crouzeix-Raviart finite element method for space discretization and implicit backward Euler scheme for time discretization. We derive an error estimate of optimal order (h + Δ t) } in a certain energy norm defined precisely in the article. We only assume the realistic regularity u t L 2 (0, T; L 2 (ω)) } and moreover the analysis is performed without any assumptions on the speed of propagation of the free boundary. We present a numerical experiment to illustrate the theoretical order of convergence derived in the article

Item Type:	Journal Article
Publication:	Computational Methods in Applied Mathematics
Publisher:	De Gruyter
Additional Information:	The copyright for this article belongs to the De Gruyter.
Keywords:	Finite Element; Parabolic Obstacle Problem
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 Feb 2023 09:08
Last Modified:	01 Feb 2023 09:08
URI:	https://eprints.iisc.ac.in/id/eprint/79676

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