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

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- by Claes Johnson, Anders Szepessy and Peter Hansbo PDF
- Math. Comp.
**54**(1990), 107-129 Request permission

## 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.## References

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## Additional Information

- © Copyright 1990 American Mathematical Society
- Journal: Math. Comp.
**54**(1990), 107-129 - MSC: Primary 65M60; Secondary 35L65, 76L05
- DOI: https://doi.org/10.1090/S0025-5718-1990-0995210-0
- MathSciNet review: 995210