A moving mesh method with variable mesh relaxation time

Authors:
Ali Reza Soheili;John M. Stockie
Affiliations:
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran;Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 16
Cited 4

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Abstract

We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time @t is employed as a regularization parameter. Previously reported results on MMPDEs have invariably employed a constant value of the parameter @t. We extend this standard approach by incorporating a variable relaxation time that is calculated adaptively alongside the solution in order to regularize the mesh appropriately throughout a computation. We focus on singular, parabolic problems involving self-similar blow-up to demonstrate the advantages of using a variable relaxation time over a fixed one in terms of accuracy, stability and efficiency.