Abstract:In this work we propose a new class of entropy consistent schemes for hyperbolic systems of conservation laws (HCL). The schemes developed so far in the classic works of Tadmor, Johnson and their collaborators start from an appropriate entropy conservative formulation of the system. Then entropy diminishing schemes are obtained by adding appropriate artificial diffusion terms. This program was based on the formulation of the HCL using the entropy variables. In this work we propose an alternative approach which has as a starting point a new mixed reformulation of the hyperbolic system which retains the original variables but still allows for conservative discretisation. The original variables are approximated directly and significant flexibility is allowed in the design of the corresponding computational algorithms. New finite element schemes are introduced and analysed. It is shown that the resulting approximations are consistent at the limit to an entropy weak and when appropriate to an entropy measure valued solution.

---

中文翻译：

---

一类新的双曲系统的熵稳定格式：有限元方法

摘要：在这项工作中，我们提出了一类新的守恒定律双曲型系统的熵一致方案。到目前为止，在Tadmor，Johnson及其合作者的经典著作中开发的方案都是从系统的适当熵保守公式开始的。然后，通过添加适当的人工扩散项来获得熵减小方案。该程序基于使用熵变量的HCL公式。在这项工作中，我们提出了一种替代方法，该方法以双曲系统的新混合重构为起点，保留了原始变量，但仍允许保守离散化。原始变量可以直接近似，并且在相应计算算法的设计中具有很大的灵活性。介绍并分析了新的有限元方案。结果表明，所得到的近似值在熵弱的极限处和在适合熵度量值的解的极限处是一致的。

---