Refinement of flexible space–time finite element meshes and discontinuous Galerkin methods
Refinement of flexible space–time finite element meshes and discontinuous Galerkin methods
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柔性时空有限元网格细化和间断伽辽金方法
DOI：
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发表时间：
2011
影响因子：
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通讯作者：
O. Steinbach
中科院分区：
文献类型：
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作者：
M. Neumüller;O. Steinbach
在本文中，我们提出了一种算法，以细化时空有限元网格所需的数值解抛物型初边值问题。该方法是基于一个分解的空间-时间圆柱有限元，这也允许一个相当一般和灵活的离散时间。这还包括随时间移动的自适应有限元网格。对于三维空间域的处理，因此四维时空圆柱体，我们描述了一种细化策略，将五元组分解成更小的。对于初边值问题的离散化，我们在空间上使用内部罚Galerkin方法，在时间上使用逆风技术。瞬态热方程的一个数值例子证实了理论预期的收敛阶。瞬态Navier-Stokes方程和自适应网格随时间移动的第一个数值结果强调了所提出的方法的适用性和灵活性。
In this paper we present an algorithm to refine space–time finite element meshes as needed for the numerical solution of parabolic initial boundary value problems. The approach is based on a decomposition of the space–time cylinder into finite elements, which also allows a rather general and flexible discretization in time. This also includes adaptive finite element meshes which move in time. For the handling of three-dimensional spatial domains, and therefore of a four-dimensional space–time cylinder, we describe a refinement strategy to decompose pentatopes into smaller ones. For the discretization of the initial boundary value problem we use an interior penalty Galerkin approach in space, and an upwind technique in time. A numerical example for the transient heat equation confirms the order of convergence as expected from the theory. First numerical results for the transient Navier–Stokes equations and for an adaptive mesh moving in time underline the applicability and flexibility of the presented approach.