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On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws. (English) Zbl 0685.65086
This paper concerns some finite element approximations to hyperbolic conservation laws. It extends some previous analysis by the authors of the so-called streamline diffusion methods by allowing to include a shock-capturing term. Convergence is then shown for scalar conservation laws and consistency with entropy solutions for systems is proven. Some numerical results are reported for the 2D compressible Euler equations.
Reviewer: P.-L.Lions

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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