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

Claes Johnson ; Anders Szepessy ; Peter Hansbo (Institutionen för tillämpad mekanik, Dynamik)
Mathematics of Computation Vol. 54 (1990), 189, p. 107-129.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2007-03-06.
CPL Pubid: 26526

 

Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Dynamik

Ämnesområden

Numerisk analys
Strömningsmekanik

Chalmers infrastruktur