Discrete Kinetic Methods for a Degenerate Parabolic Equation in Dimension Two.

Aregba-Driollet, Denise

doi:10.1007/978-3-540-34288-5_31

Denise Aregba-Driollet³

1408 Accesses

Abstract

We design finite volume schemes for two dimensional parabolic degenerate systems by using a kinetic, formally BGK, approach. The hyperbolic and parabolic parts are not splitted and the schemes are Riemann solver free. Moreover the spatial discretization can be written analytically, so that the implementation is easy. Some numerical tests are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 109.00; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

Aregba-Driollet, D., Natalini, R., Tang, S.: Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems. Math. Comp., 73, 63–94 (2004)
Article MATH MathSciNet Google Scholar
Bouchut, F., Guarguaglini, F., Natalini, R.: Diffusive BGK Approximations for Nonlinear Multidimensional Parabolic Equations, Indiana Univ. Math. J., 49, 723–749, (2000)
Article MATH MathSciNet Google Scholar
Cavalli, F., Naldi, G., Semplice, M.: Parallel algorithms for non-linear diffusion by using relaxation approximation. ENUMATH2005
Google Scholar
Eymard, R., Gallouet, T., Herbin, R., Michel, A: Convergence of a finite volume scheme for nonlinear degenerate parabolic equations. Numer. Math., 92, no. 1, 41–82 (2002)
Article MATH MathSciNet Google Scholar
Harten, A., Lax, P.D., van Leer, B.: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev., 25, no. 1, 35–61 (1983).
Article MATH MathSciNet Google Scholar
Jin, S., Xin, Z.: The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math 48, 235–277 (1995).
Article MATH MathSciNet Google Scholar
Lattanzio, C., Natalini, R.:Convergence of diffusive BGK approximations for parabolic systems, Proc. Roy. Soc. Edinburgh Sect. A, 132, no. 2, 341–358 (2002)
Article MATH MathSciNet Google Scholar
Michel, A., Vovelle, J.: Entropy formulation for parabolic degenerate equations with general Dirichlet boundary conditions and application to the convergence of FV methods. SIAM J. Numer. Anal. 41, no. 6, 2262–2293 (2003)
Article MATH MathSciNet Google Scholar

Download references

Author information

Authors and Affiliations

IMB, MAB, Université Bordeaux 1, 351 cours de la Libération, 33405, Talence cedex, France
Denise Aregba-Driollet

Authors

Denise Aregba-Driollet
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Departamento de Matemática Aplicada Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706, Santiago de Compostela, Spain
Alfredo Bermúdez de Castro , Dolores Gómez & Peregrina Quintela , &
Departamento de Matématica Aplicada, Escola Politécnica Superior, 27002, Lugo, Spain
Pilar Salgado

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Aregba-Driollet, D. (2006). Discrete Kinetic Methods for a Degenerate Parabolic Equation in Dimension Two.. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_31

Download citation

DOI: https://doi.org/10.1007/978-3-540-34288-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34287-8
Online ISBN: 978-3-540-34288-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Publish with us

Policies and ethics