On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws

Claes Johnson, Anders Szepessy, Peter Hansbo
1990 Mathematics of Computation  
We extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shockcapturing 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
more » ... g 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.
doi:10.1090/s0025-5718-1990-0995210-0 fatcat:g6bjfzgqefhehdge7mp4hzgpsu