Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

Ganesan, Sashikumaar and Tobiska, Lutz (2013) Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems. In: APPLIED MATHEMATICS AND COMPUTATION, 219 (11). pp. 6182-6196.

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Abstract

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICS AND COMPUTATION
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copyright for this article belongs to ELSEVIER SCIENCE INC, NEW YORK
Keywords:	Operator-splitting method;Finite element method;Parabolic equations;High-dimensional problems
Department/Centre:	Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre
Date Deposited:	18 Mar 2013 05:26
Last Modified:	18 Mar 2013 05:26
URI:	http://eprints.iisc.ac.in/id/eprint/46072

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