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On the convergence of a finite element method for a nonlinear hyperbolic conservation law. (English) Zbl 0634.65075
An upstream Petrov-Galerkin method with shock capturing is introduced for systems of nonlinear conservation laws. It is shown that for the nonviscous Burgers equation the method converges to an entropy solution provided that the finite-element solutions are uniformly bounded. Computational examples are given for the nonviscous Burgers equation showing the effect of various choices of the shock-capturing parameter.
Reviewer: G.Hedstrom

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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