dc.contributor.author Budd, Chris J. dc.contributor.author Huang, Weizhang dc.contributor.author Russell, Robert D. dc.date.accessioned 2015-02-26T17:36:19Z dc.date.available 2015-02-26T17:36:19Z dc.date.issued 1996-03-01 dc.identifier.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. en_US dc.identifier.uri http://hdl.handle.net/1808/16883 dc.description This is the published version, also available here: http://dx.doi.org/10.1137/S1064827594272025. en_US dc.description.abstract 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. en_US dc.publisher Society for Industrial and Applied Mathematics en_US dc.subject blow-up solution en_US dc.subject moving mesh en_US dc.subject scaling invariance en_US dc.title Moving Mesh Methods for Problems with Blow-Up en_US dc.type Article kusw.kuauthor Huang, Weizhang kusw.kudepartment Mathematics en_US dc.identifier.doi 10.1137/S1064827594272025 kusw.oaversion Scholarly/refereed, publisher version kusw.oapolicy This item does not meet KU Open Access policy criteria. dc.rights.accessrights openAccess
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