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    A Class of Adaptive Multiresolution Ultra-Weak Discontinuous Galerkin Methods for Some Nonlinear Dispersive Wave Equations

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    2104.05523.pdf (12.05Mb)
    Date
    2022-03-29
    Author
    Huang, Juntao
    Liu, Yong
    Liu, Yuan
    Tao, Zhanjing
    Cheng, Yingda
    Metadata
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    Citation
    Scott, H., Huang, W., Andra, K., Mamillapalli, S., Gonti, S., Day, A., . . . Taylor, D. J. (2022). Structure of the Anthrax Protective Antigen D425A Dominant Negative Mutant Reveals a Stalled Intermediate State of Pore Maturation. Journal of Molecular Biology, 434(9). https://doi.org/https://doi.org/10.1016/j.jmb.2022.167548
    Abstract
    In this paper, we propose a class of adaptive multiresolution (also called the adaptive sparse grid) ultra-weak discontinuous Galerkin (UWDG) methods for solving some nonlinear dispersive wave equations including the Korteweg-de Vries (KdV) equation and its two-dimensional generalization, the Zakharov-Kuznetsov (ZK) equation. The UWDG formulation, which relies on repeated integration by parts, was proposed for the KdV equation in [7]. For the ZK equation, which contains mixed derivative terms, we develop a new UWDG formulation. The L2 stability is established for this new scheme on regular meshes, and the optimal error estimate with a novel local projection is obtained for a simplified ZK equation. Adaptivity is achieved based on multiresolution and is particularly effective for capturing solitary wave structures. Various numerical examples are presented to demonstrate the accuracy and capability of our methods.
    Description
    Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article.
    URI
    https://doi.org/10.1137/21M1411391
    https://soar.wichita.edu/handle/10057/23319
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