On the stability of a family of finite element methods for hyperbolic problems
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- by Gerard R. Richter PDF
- Math. Comp. 71 (2002), 527-535 Request permission
Abstract:
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.References
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Additional Information
- Gerard R. Richter
- Affiliation: Department of Computer Science, Rutgers University, New Brunswick, New Jersey 08903
- Email: richter@cs.rutgers.edu
- Received by editor(s): December 8, 1999
- Received by editor(s) in revised form: August 8, 2000
- Published electronically: May 22, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 527-535
- MSC (2000): Primary 65M60, 65M12
- DOI: https://doi.org/10.1090/S0025-5718-01-01334-5
- MathSciNet review: 1885613