A moving mesh method with variable relaxation time

Details A moving mesh method with variable relaxation time A moving mesh method with variable relaxation time

2006-02-17

arxiv.org/abs/math/0602376v1

Applied Numerical Mathematics, 58(3):249-263, 2008

Mathematics

Numerical Analysis

21 pages

Scientific paper

10.1016/j.apnum.2006.11.014

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 \tau is employed as a regularization parameter. Previously reported results on MMPDEs have invariably employed a constant value of the parameter \tau. 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 problems involving self-similar blow-up to demonstrate the advantages of using a variable relaxation ime over a fixed one in terms of accuracy, stability and efficiency.

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