期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 197, 期 13-16, 页码 1305-1322出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2007.11.006
关键词
hyperbolic wave equation; stabilized finite element methods; orthogonal subscales
The purpose of this paper is to present a finite element approximation of the scalar hyperbolic wave equation written in mixed form, that is, introducing an auxiliary vector field to transform the problem into a first-order problem in space and time. We explain why the standard Galerkin method is inappropriate to solve this problem, and propose as alternative a stabilized finite element method that can be cast in the variational multiscale framework. The unknown is split into its finite element component and a remainder, referred to as subscale. As original features of our approach, we consider the possibility of letting the subscales to be time dependent and orthogonal to the finite element space. The formulation depends on algorithmic parameters whose expression is proposed from a heuristic Fourier analysis. (c) 2007 Elsevier B.V. All rights reserved.
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