Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics
Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics
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DOI：
10.1093/imanum/drv052
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
J. Giesselmann;T. Pryer
中科院分区：
文献类型：
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作者：
J. Giesselmann;T. Pryer
我们给出了一个后验分析的半离散不连续Galerkin计划近似解决方案的多相弹性动力学模型，其中涉及的能量密度不仅取决于应变，而且应变梯度。分析中的一个关键组成部分是[Giesselmann 2014]中开发的约化相对熵稳定性框架。这个框架允许能量类型参数应用于连续函数。由于我们提倡使用不连续Galerkin方法，因此我们使用两种重建方法，一种是离散重建[Makridakis and Nochetto 2006]，另一种是椭圆重建[Makridakis and Nochetto 2003]，以在这种情况下应用约化相对熵框架。
We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in [Giesselmann 2014]. This framework allows energy type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions [Makridakis and Nochetto 2006] and a set of elliptic reconstructions [Makridakis and Nochetto 2003] to apply the reduced relative entropy framework in this setting.