On the Convergence of Shock-Capturing Streamline Diffusion Finite Element Methods for Hyperbolic Conservation Laws
- 1 January 1990
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 54 (189) , 107-129
- https://doi.org/10.2307/2008684
Abstract
We extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock-capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the mesh size. With this term present, we prove a maximum norm bound for finite element solutions of Burgers' equation and thus complete an earlier convergence proof for this equation. We further prove, using entropy variables, that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality associated with the entropy variables. Results of some numerical experiments for the time-dependent compressible Euler equations in two dimensions are also reported.Keywords
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