Moving Mesh Methods for Problems with Blow-Up

View/ Open
Issue Date
1996-03-01Author
Budd, Chris J.
Huang, Weizhang
Russell, Robert D.
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the qualitative behaviour in the blow-up region, and the use of nonuniform meshes is essential. We consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs).Specifically, the underlying PDE and the MMPDE are solved for the blow-up solution and the computational mesh simultaneously. Motivated by the desire for the MMPDE to preserve the scaling invariance of the underlying problem, we study the effect of different choices of MMPDEs and monitor functions. It is shown that for suitable ones the MMPDE solution evolves towards a. (moving) mesh which close to the blow-up point automatically places the mesh points in such a manner that the ignition kernel, which is well known to be a natural coordinate in describing the behaviour of blow-up, approaches a constant as $t \to T$ (the blow-up time). Several numerical examples are given to verify the theory for these MMPDE methods and to illustrate their efficacy.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/S1064827594272025.
Collections
Citation
Budd, Chris J., Huang, Weizhang., Russell, Robert D. "Moving mesh methods for problems with blow-up." SIAM J. Sci. Comput., 17(2), 305–327. (23 pages). http://dx.doi.org/10.1137/S1064827594272025.
Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.