Foundations of Finite Element Methods for Wave Equations of Maxwell Type
Foundations of Finite Element Methods for Wave Equations of Maxwell Type
复制标题
麦克斯韦型波动方程的有限元方法基础
DOI：
10.1007/978-3-642-00585-5_17
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
S. Christiansen
中科院分区：
文献类型：
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作者：
S. Christiansen
本文的第一部分是波动方程Galerkin逼近理论的概述。它处理收敛理论的线性二阶发展方程，包括研究的一致性和特征值逼近。我们强调微分算子，如旋度，其中有大的内核，并使用L2稳定插值保持它们。第二部分提供了一个设置的构造有限元空间的微分形式的细胞复合体。包括同调和张量代数以及微分和离散几何的材料。惠特尼形式，他们的双曲型，他们的高阶版本，他们的张量积和他们的hp版本都适合这个框架。
The first part of this paper is an overview of the theory of approximation of wave equations by Galerkin methods. It treats convergence theory for linear second order evolution equations and includes studies of consistency and eigenvalue approximation. We emphasize differential operators, such as the curl, which have large kernels, and use L2-stable interpolators preserving them. The second part provides a setting for the construction of finite element spaces of differential forms on cellular complexes. Material on homological and tensor algebra as well as differential and discrete geometry is included. Whitney forms, their duals, their high order versions, their tensor products and their hp-versions all fit into this framework.