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On the convergence of shock capturing streamline diffusion finite-element methods for hyperbolic conservation-laws
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
1990 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 54, no 189, 107-129 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
1990. Vol. 54, no 189, 107-129 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-15872DOI: 10.2307/2008684ISI: A1990CM47400006OAI: oai:DiVA.org:hj-15872DiVA: diva2:440251
Available from: 2011-09-12 Created: 2011-08-16 Last updated: 2012-02-07Bibliographically approved

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