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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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Official URL: http://dx.doi.org/10.1016/j.amc.2012.12.027

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
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 Research > Supercomputer Education & Research Centre
Depositing User: Francis Jayakanth
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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