Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems

Authors:
D. Aregba-Driollet;R. Natalini;S. Tang
Affiliations:
Mathématiques Appliquées De Bordeaux, Université Bordeaux 1, 351 Cours De La Libération, F-33405 Talence, France;Istituto Per Le Applicazioni Del Calcolo "M. Picone", Consiglio Nazionale Delle Ricerche, Viale Del Policlinico 137, I-00161 Roma, Italia;Department of Mechanics and Engineering Sciences, Peking University, Beijing 100871, People's Republic of China and Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konztanz, ...
Venue:
Mathematics of Computation
Year:
2004

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Abstract

We design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection. These schemes are based on discrete BGK models where both characteristic velocities and the source-term depend singularly on the relaxation parameter. General stability conditions are derived, and convergence is proved to the entropy solutions for scalar equations.