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On the stability of a family of finite element methods for hyperbolic problems
Authors:Gerard R. Richter.
Affiliation:Department of Computer Science, Rutgers University, New Brunswick, New Jersey 08903
Abstract:

We consider a family of tensor product finite element methods for hyperbolic equations in $R^{N}$, $Nge 2$, 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.

Keywords:Finite elements   hyperbolic   explicit
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