A SPECTRAL VISCOSITY METHOD BASED ON HERMITEFUNCTIONS FOR NONLINEAR CONSERVATION LAWS

JULIAN AGUIRRE; JUDITH RIVAS

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A SPECTRAL VISCOSITY METHOD BASED ON HERMITEFUNCTIONS FOR NONLINEAR CONSERVATION LAWS

机译：基于遗传函数的非线性守恒定律的光谱黏度方法

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摘要

We consider the approximation by a spectral method of the solution of the Cauchyproblem for a scalar conservation law in one dimension posed in the whole real line. We analyze a.spectral viscosity method in which the orthogonal basis considered is the one of Hermite functions.We prove the convergence of the approximate solution to the unique entropy solution of the problemby using compensated compactness arguments.

机译：我们考虑通过谱方法逼近整个实线中一维标量守恒定律的柯西问题的解。我们分析了一种以正交基为Hermite函数的谱粘度方法。通过使用补偿的紧致性参数，证明了近似解对问题唯一熵解的收敛性。

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《SIAM Journal on Numerical Analysis》 |2009年第2期|共19页
作者
JULIAN AGUIRRE; JUDITH RIVAS;
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正文语种 eng
中图分类数值分析;
关键词
hyperbolic conservation laws; Hermite functions; spectral methods; spectral vis-cosity; compensated compactness;

机译：双曲守恒律;赫米特函数;光谱方法;光谱粘度;补偿密实度;

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专利

1. A SPECTRAL VISCOSITY METHOD BASED ON HERMITEFUNCTIONS FOR NONLINEAR CONSERVATION LAWS [J] . JULIAN AGUIRRE, JUDITH RIVAS SIAM Journal on Numerical Analysis . 2009,第2期

机译：基于遗传函数的非线性守恒定律的光谱黏度方法
2. Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws [J] . Xue Luo Applied numerical mathematics . 2018,第jana期

机译：非线性守恒律的广义Hermite函数谱粘度法
3. Super spectral viscosity method for nonlinear conservation laws [J] . 马和平, 李会元上海大学学报：英文版 . 2006,第001期

机译：非线性守恒律的超光谱粘度法
4. Entropy Viscosity Method for High-Order Approximations of Conservation Laws [C] . J.L. Guermond, R. Pasquetti International conference on spectral and high order methods . 2011

机译：熵粘度法，用于高级保护法的近似
5. Numerical solutions of hyperbolic conservation laws: Incorporating multi-resolution viscosity methods into the finite element framework. [D] . Calhoun-Lopez, Marcus. 2003

机译：双曲守恒律的数值解：将多分辨率黏度方法纳入有限元框架。
6. Discontinuous Galerkin methods for nonlinear scalar hyperbolic conservation laws: divided difference estimates and accuracy enhancement [O] . Xiong Meng, Jennifer K. Ryan -1

机译：非线性标量双曲守恒定律的不连续Galerkin方法：差分估计和精度提高
7. Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws [O] . Luo, Xue 2017

机译：具有广义Hermite函数的谱粘性方法非线性守恒定律
8. Analysis of the Spectral Vanishing Viscosity Method for Periodic Conservation Laws [R] . Maday, Y., Tadmor, E. 1988

机译：周期守恒律的光谱消失粘性方法分析

A SPECTRAL VISCOSITY METHOD BASED ON HERMITEFUNCTIONS FOR NONLINEAR CONSERVATION LAWS

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