论文标题
高阶不连续的剪切有限元方法，用于线性双曲线保护法，界面
High order discontinuous cut finite element methods for linear hyperbolic conservation laws with an interface
论文作者
论文摘要
我们基于不连续的盖尔金框架，开发出不同订单的有限元方法的家族，用于在一个和两个空间尺寸中具有固定接口的双曲线保护定律，以及在一个空间维度中移动接口。界面条件弱施加，因此可以确保保护和稳定性。在空间中开发了一个不连续元素的CUTFEM，并与线性对流问题的标准显式时间稳定方案结合在一起，以及带有固定接口的声波问题。在移动界面的情况下，我们根据线性对流问题的时空和时间上的不连续元素提出了一个时空cutfem。我们表明，拟议的Cutfem是保守和能量稳定的。对于固定接口案例，证明了先验错误估计。一个和两个空间维度的数值计算都支持分析，此外表明所提出的方法具有预期的精度。
We develop a family of cut finite element methods of different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, and for moving interfaces in one space dimension. Interface conditions are imposed weakly and so that both conservation and stability are ensured. A CutFEM with discontinuous elements in space is developed and coupled to standard explicit time-stepping schemes for linear advection problems and the acoustic wave problem with stationary interfaces. In the case of moving interfaces, we propose a space-time CutFEM based on discontinuous elements both in space and time for linear advection problems. We show that the proposed CutFEM are conservative and energy stable. For the stationary interface case an a priori error estimate is proven. Numerical computations in both one and two space dimensions support the analysis, and in addition demonstrate that the proposed methods have the expected accuracy.
