On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws
Artikel i vetenskaplig tidskrift, 1990

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 meh size. With this term present, we prove a maximum norm bound for finite element solutionsof Burgers' equation an 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 asociated with the entropy variables. Results of some numerical experiments for the time-dependent compressible Euler equations in two dimensions are also reported.

Författare

Claes Johnson

Anders Szepessy

Peter F G Hansbo

Dynamik

Mathematics of Computation

Vol. 54 189 107-129

Ämneskategorier

Beräkningsmatematik

Strömningsmekanik och akustik

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2017-10-06