An energy-based discontinuous Galerkin method for semilinear wave equations

Appelo Daniel; Hagstrom Thomas; Wang Qi; Zhang Lu

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An energy-based discontinuous Galerkin method for semilinear wave equations

机译：半线性波动方程的基于能量的不连续的Galerkin方法

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摘要

We generalize the energy-based discontinuous Galerkin method proposed in [1] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical experiments demonstrating optimal convergence for certain choices of the interelement fluxes. Applications to the sine-Gordon equation include simulations of breathers, kink, and anti-kink solitons. (C) 2020 Elsevier Inc. All rights reserved.

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《Journal of Computational Physics》 |2020年第1期|共25页
作者
Appelo Daniel; Hagstrom Thomas; Wang Qi; Zhang Lu;
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作者单位

Univ Colorado Dept Appl Math Boulder CO 80309 USA;

Southern Methodist Univ Dept Math Dallas TX 75275 USA;

Southwestern Univ Finance &

Econ Dept Math 555 Liutai Ave Chengdu 611130 Sichuan Peoples R China;

Southern Methodist Univ Dept Math Dallas TX 75275 USA;

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原文格式 PDF
正文语种 eng
中图分类数学物理方法;
关键词
Discontinuous Galerkin; Semilinear wave equation; Upwind flux;

机译：不连续的Galerkin;半线性波浪方程;Upwind助焊剂;

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专利

1. An energy-based discontinuous Galerkin method for semilinear wave equations [J] . Appelo Daniel, Hagstrom Thomas, Wang Qi, Journal of Computational Physics . 2020,第1期

机译：半线性波动方程的基于能量的不连续的Galerkin方法
2. AN ENERGY-BASED DISCONTINUOUS GALERKIN METHOD FOR THE WAVE EQUATION WITH ADVECTION [J] . Zhang Lu, Hagstrom Thomas, Appelo Daniel SIAM Journal on Numerical Analysis . 2019,第5期

机译：一种基于能量的不连续Galerkin方法，用于平流的波浪方程
3. An Improved Vector Wave Equation-Based Discontinuous Galerkin Time Domain Method and Its Hybridization With Maxwell’s Equation-Based Discontinuous Galerkin Time Domain Method [J] . Cheng-Yi Tian, Yan Shi, Chi Hou Chan Antennas and Propagation, IEEE Transactions on . 2018,第11期

机译：改进的基于矢量波方程的不连续Galerkin时域方法及其与麦克斯韦基于方程的不连续Galerkin时域方法的混合
4. Wave- Based Discontinuous Galerkin Methods for the Linearized Euler Equations in the Frequency Domain [C] . G. Gabard . 2007

机译：频域中线性化Euler方程的基于波的间断Galerkin方法
5. Discontinuous Galerkin methods for Hamilton-Jacobi equations and high-dimensional elliptic equations [D] . Wang, Zixuan. 2015

机译：汉密尔顿 - Jacobi方程和高维椭圆方程的不连续的Galerkin方法
6. Comparison of reduced models for blood flow using Runge–Kutta discontinuous Galerkin methods [O] . Charles Puelz, Sunčica Čanić, Béatrice Rivière, -1

机译：使用Runge-Kutta不连续Galerkin方法简化的血流模型的比较
7. An energy-based discontinuous Galerkin method for semilinear wave equations [O] . Daniel Appelö, Thomas Hagstrom, Qi Wang, 2020

机译：用于半线性波动方程的基于能量的不连续的Galerkin方法

An energy-based discontinuous Galerkin method for semilinear wave equations

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