A splitting moving mesh method for 3-D quenching and blow-up problems

Kewei Liang, Ping Lin

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    We present a splitting moving mesh method for multi-dimensional reaction-diffusion problems with nonlinear forcing terms over rectangular domains.The structure of the adaptive algorithm is an elegant combination of an operator splitting and one-dimensional moving mesh. It is motivated by the nature of splitting method, which splits a multi-dimensional problems into a few one-dimensional problems. Therefore, the temporal and the spatial adaptations are adopted based on one-dimensional arc-length equidistributed rule. The method not only keeps the advantage of splitting methods on reducing computational cost but also simplifies the implementation of moving mesh techniques. The method is first presented in [20] for the 2-D quenching problems using Peaceman-Rachford splitting. In this paper, we apply the splitting moving mesh method to both the 3-D blow-up and the 3-D quenching singularity using Douglas splitting. 3-D numerical examples will be given to demonstrate the good performance of the method.
    Original languageEnglish
    Title of host publicationRecent advances in adaptive computation: proceedings of the International Conference on Recent Advances in Adaptive Computation, Hangzhou, China, May 24-28, 2004
    EditorsZ.-C. Shi, Z. Chen, T. Tang, D. Yu
    PublisherAmerican Mathematical Society
    Pages311-324
    Number of pages14
    ISBN (Print)9780821836620
    Publication statusPublished - 2005

    Publication series

    NameContemporary mathematics
    Number383

    Keywords

    • Reaction-diffusion
    • Splitting methods

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  • Cite this

    Liang, K., & Lin, P. (2005). A splitting moving mesh method for 3-D quenching and blow-up problems. In Z-C. Shi, Z. Chen, T. Tang, & D. Yu (Eds.), Recent advances in adaptive computation: proceedings of the International Conference on Recent Advances in Adaptive Computation, Hangzhou, China, May 24-28, 2004 (pp. 311-324). (Contemporary mathematics; No. 383). American Mathematical Society. http://copac.ac.uk/crn/72013413396/html