Convergence of a Shock-Capturing Streamline Diffusion Finite Element Method for a Scalar Conservation Law in Two Space Dimensions
- 1 October 1989
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 53 (188) , 527-545
- https://doi.org/10.2307/2008718
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.Keywords
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