论文标题
混合有限元 - 保护法的有限体积方法
A hybrid finite element - finite volume method for conservation laws
论文作者
论文摘要
我们提出了一种基于解决方案连续近似的保护定律的任意高阶精确数值方法。自由度是细胞界面和溶液矩值的点值。最低（$ 3^\ text {rd} $）订购此方法将减少为Active Flux方法。通过将保护定律整合到细胞上，通过零件整合并在细胞界面上采用连续性来立即实现矩的更新。我们提出了两种方法可以在时间上更新点值的方式：要么首先派生使用有限差异类型公式来近似空间衍生物的半差异方法，然后集成此方法，例如。使用Runge-Kutta方案，或使用基于特征的更新，该更新灵感来自原始（完全离散的）活动通量方法。我们分析了所得方法的稳定性和准确性。
We propose an arbitrarily high-order accurate numerical method for conservation laws that is based on a continuous approximation of the solution. The degrees of freedom are point values at cell interfaces and moments of the solution inside the cell. To lowest ($3^\text{rd}$) order this method reduces to the Active Flux method. The update of the moments is achieved immediately by integrating the conservation law over the cell, integrating by parts and employing the continuity across cell interfaces. We propose two ways how the point values can be updated in time: either by first deriving a semi-discrete method that uses a finite-difference-type formula to approximate the spatial derivative, and integrating this method e.g. with a Runge-Kutta scheme, or by using a characteristics-based update, which is inspired by the original (fully discrete) Active Flux method. We analyze stability and accuracy of the resulting methods.
