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