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Journal of Scientific Computing

Erschienen in:

01.10.2020

An Adaptive Multiresolution Interior Penalty Discontinuous Galerkin Method for Wave Equations in Second Order Form

verfasst von: Juntao Huang, Yuan Liu, Wei Guo, Zhanjing Tao, Yingda Cheng

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2020

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Abstract

In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) discontinuous Galerkin (DG) methods for simulating scalar wave equations in second order form in space. The two key ingredients of the schemes include an interior penalty DG formulation in the adaptive function space and two classes of multiwavelets for achieving multiresolution. In particular, the orthonormal Alpert’s multiwavelets are used to express the DG solution in terms of a hierarchical structure, and the interpolatory multiwavelets are further introduced to enhance computational efficiency in the presence of variable wave speed or nonlinear source. Some theoretical results on stability and accuracy of the proposed method are presented. Benchmark numerical tests in 2D and 3D are provided to validate the performance of the method.

Vorheriger Artikel A Quasi-Conservative Discontinuous Galerkin Method for Solving Five Equation Model of Compressible Two-Medium Flows

Nächster Artikel A Divergence-Conforming DG-Mixed Finite Element Method for the Stationary Boussinesq Problem

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Titel: An Adaptive Multiresolution Interior Penalty Discontinuous Galerkin Method for Wave Equations in Second Order Form
verfasst von: Juntao Huang
Yuan Liu
Wei Guo
Zhanjing Tao
Yingda Cheng
Publikationsdatum: 01.10.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01322-w

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