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Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems


Authors: D. Aregba-Driollet, R. Natalini and S. Tang
Journal: Math. Comp. 73 (2004), 63-94
MSC (2000): Primary 65M06; Secondary 76M20, 76RXX, 82C40
DOI: https://doi.org/10.1090/S0025-5718-03-01549-7
Published electronically: August 26, 2003
MathSciNet review: 2034111
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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.


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Additional Information

D. Aregba-Driollet
Affiliation: Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, F-33405 Talence, France
Email: aregba@math.u-bordeaux.fr

R. Natalini
Affiliation: Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, I–00161 Roma, Italia
Email: natalini@iac.rm.cnr.it

S. Tang
Affiliation: Department of Mechanics and Engineering Sciences, Peking University, Beijing 100871, People’s Republic of China and Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany
Email: maotang@pku.edu.cn; tangs@fmi.uni-konstanz.de

DOI: https://doi.org/10.1090/S0025-5718-03-01549-7
Received by editor(s): November 21, 2000
Received by editor(s) in revised form: January 11, 2002
Published electronically: August 26, 2003
Additional Notes: Work partially supported by European TMR projects HCL # ERB FMRX CT96 0033 and NPPDE # ERB FMRX CT98 0201, Chinese Special Funds for Major State Basic Research Project, and NSFC
Article copyright: © Copyright 2003 American Mathematical Society