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A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations
Huang, Juntao Liu, Yong Liu, Yuan Tao, Zhanjing Cheng, Yingda
Huang, Juntao
Liu, Yong
Liu, Yuan
Tao, Zhanjing
Cheng, Yingda
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2022-03-29
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Article
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Keywords
Sparse grid,Discontinuous Galerkin,Dispersive equations,Multiresolution,Adaptive,Error estimate
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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.
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Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article.
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Society for Industrial and Applied Mathematics Publications
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SIAM Journal on Scientific Computing
v.44 no.2
v.44 no.2
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1064-8275