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Mathematics of Computation

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On the stability of a family of finite element methods for hyperbolic problems

Author: Gerard R. Richter
Journal: Math. Comp. 71 (2002), 527-535
MSC (2000): Primary 65M60, 65M12
Published electronically: May 22, 2001
MathSciNet review: 1885613
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We consider a family of tensor product finite element methods for hyperbolic equations in $R^{N}$, $N\ge 2$, which are explicit and generate a continuous approximate solution. The base case $N=2$ (an extension of the box scheme to higher order) is due to Winther, who proved stability and optimal order convergence. By means of a simple counterexample, we show that, for linear approximation with $N \ge 3$, the corresponding methods are unstable.

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Additional Information

Gerard R. Richter
Affiliation: Department of Computer Science, Rutgers University, New Brunswick, New Jersey 08903

Keywords: Finite elements, hyperbolic, explicit
Received by editor(s): December 8, 1999
Received by editor(s) in revised form: August 8, 2000
Published electronically: May 22, 2001
Article copyright: © Copyright 2001 American Mathematical Society