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

DOI:
https://doi.org/10.1090/S0025-5718-01-01334-5

Published electronically:
May 22, 2001

MathSciNet review:
1885613

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We consider a family of tensor product finite element methods for hyperbolic equations in , , which are explicit and generate a continuous approximate solution. The base case (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 , 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

Email:
richter@cs.rutgers.edu

DOI:
https://doi.org/10.1090/S0025-5718-01-01334-5

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