On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws
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.
- Publication:
-
Mathematics of Computation
- Pub Date:
- January 1990
- DOI:
- 10.1090/S0025-5718-1990-0995210-0
- Bibcode:
- 1990MaCom..54..107J
- Keywords:
-
- Finite element method;
- conservation laws;
- convergence streamline diffusion;
- shock-capturing;
- entropy variables