Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
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DOI：
10.4208/cicp.oa-2019-0047
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发表时间：
2020-06
影响因子：
3.7
通讯作者：
Stephan Gerster and Michael Herty
中科院分区：
文献类型：
--
作者：
Stephan Gerster and Michael Herty
使用随机伽辽金方法在广义多项式混沌展开中展开感兴趣的随机量。双曲微分方程的应用通常不会将双曲性转移到截断级数展开式的系数上。对于 Haar 基和分段线性多小波，我们通过使用 Roe 变量变换给出一维浅水方程系数组的凸熵。这允许获得双曲性、适定性和能量估计。 AMS 科目分类：35L65、54C70、58J45、70S10、37L45、35R60
Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. An application to hyperbolic differential equations does in general not transfer hyperbolicity to the coefficients of the truncated series expansion. For the Haar basis and for piecewise linear multiwavelets we present convex entropies for the systems of coefficients of the one-dimensional shallow water equations by using the Roe variable transform. This allows to obtain hyperbolicity, wellposedness and energy estimates. AMS subject classifications: 35L65, 54C70, 58J45, 70S10, 37L45, 35R60