论文标题
在移动域上的PDE上的几何较高阶段不实现的时空方法
Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains
论文作者
论文摘要
在本文中，我们提出了针对空间和时间高度准确性的移动域上的部分微分方程的新几何时空有限元方法。作为模型问题，研究了移动域上的对流扩散问题。对于几何级别的准确性，我们在背景时空张量产品网格上应用参数映射。关于时间的离散，我们考虑不连续的盖尔金，以及相关的连续（Petrov-）Galerkin和Galerkin搭配方法。为了稳定下的剪切配置，作为后两个方案所需的扩展机制，采用了幽灵惩罚稳定。该文章重点放在允许实现平稳域的强大但高阶几何处理的技术上。我们在一系列数值实验中研究了相应方法的计算特性。这些包括在不同维度上针对空间和时间上不同多项式程度的研究，从而验证了两个变量的较高级准确性。
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion problem on a moving domain is studied. For geometrically higher order accuracy, we apply a parametric mapping on a background space-time tensor-product mesh. Concerning discretisation in time, we consider discontinuous Galerkin, as well as related continuous (Petrov-)Galerkin and Galerkin collocation methods. For stabilisation with respect to bad cut configurations and as an extension mechanism that is required for the latter two schemes, a ghost penalty stabilisation is employed. The article puts an emphasis on the techniques that allow to achieve a robust but higher order geometry handling for smooth domains. We investigate the computational properties of the respective methods in a series of numerical experiments. These include studies in different dimensions for different polynomial degrees in space and time, validating the higher order accuracy in both variables.
