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    Moving Mesh Methods for Problems with Blow-Up

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    HuangW_SJoSC_17(2)305.pdf (2.445Mb)
    Issue Date
    1996-03-01
    Author
    Budd, Chris J.
    Huang, Weizhang
    Russell, Robert D.
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
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    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.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1137/S1064827594272025.
    URI
    http://hdl.handle.net/1808/16883
    DOI
    https://doi.org/10.1137/S1064827594272025
    Collections
    • Mathematics Scholarly Works [273]
    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.

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    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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