Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations
BENDAHMANE, Mostafa
Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA]
Institut de Mathématiques de Bordeaux [IMB]
Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA]
Institut de Mathématiques de Bordeaux [IMB]
BENDAHMANE, Mostafa
Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Journal of Hyperbolic Differential Equations. 2010, vol. 7, n° 1, p. 1--67
World Scientific Publishing
English Abstract
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn ...Read more >
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the construction and analysis of discrete duality finite volume schemes (in the spirit of Domelevo and Omn`es [43]) for these problems in two and three spatial dimensions. We derive a series of discrete duality formulas and entropy dissipation inequalities for the schemes. We establish the existence of solutions to the discrete problems, and prove that sequences of approximate solutions generated by the discrete duality finite volume schemes converge strongly to the entropy solution of the continuous problem. The proof revolves around basic a priori estimates, the discrete duality features, Minty–Browder type arguments, and “hyperbolic” L∞ weak-* compactness arguments (i.e. propagation of compactness along the lines of Tartar, DiPerna, . . . ). Our results cover the case of non-Lipschitz nonlinearities.Read less <
Keywords
convergence
English Keywords
Degenerate hyperbolic-parabolic equation
conservation law
Leray–Lions type operator
non-Lipschitz flux
entropy solution
existence
uniqueness
finite volume scheme
discrete duality
convergence.
Origin
Hal imported