Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems
复制标题
双曲系统的不变域和一阶连续有限元逼近
DOI：
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发表时间：
2015
影响因子：
2.9
通讯作者：
B. Popov
中科院分区：
文献类型：
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作者：
J. Guermond;B. Popov
本文提出了一种在非均匀网格上使用前向欧拉时间推进和连续有限元求解任意空间维一般双曲型方程组的数值方法。该方法的属性是基于引入人工耗散，定义，使任何凸不变集包含的初始数据是一个不变域的方法。证明了只要CFL条件成立，任何双曲型方程组都具有不变域性质。对于系统的每一个容许熵，该解也满足一个离散熵不等式。该方法在空间上具有形式上的一阶精度，在时间上可以通过强保稳定算法得到高阶精度。这种方法将引用{Hoff_1979，Hoff_1985}和引用{Frid_2001}的工作扩展到连续有限元。
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an artificial dissipation that is defined so that any convex invariant sets containing the initial data is an invariant domain for the method. The invariant domain property is proved for any hyperbolic system provided a CFL condition holds. The solution is also shown to satisfy a discrete entropy inequality for every admissible entropy of the system. The method is formally first-order accurate in space and can be made high-order in time by using Strong Stability Preserving algorithms. This technique extends to continuous finite elements the work of cite{Hoff_1979,Hoff_1985}, and cite{Frid_2001}.