Convergence of a shock-capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions

Author:
Anders Szepessy

Journal:
Math. Comp. **53** (1989), 527-545

MSC:
Primary 65M60

MathSciNet review:
979941

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Abstract: We prove a convergence result for a shock-capturing streamline diffusion finite element method applied to a time-dependent scalar nonlinear hyperbolic conservation law in two space dimensions. The proof is based on a uniqueness result for measure-valued solutions by DiPerna. We also prove an almost optimal error estimate for a linearized conservation law having a smooth exact solution.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0979941-6

Article copyright:
© Copyright 1989
American Mathematical Society