Discrete entropy structures in nonlinear diffusive evolution equations

01.04.2012 - 31.07.2016
Forschungsförderungsprojekt
Time-dependent partial differential equations from science and technology typically contain some structural information reflecting inherent physical properties such as positivity, mass and energy conservation, or entropy dissipation. These properties are of major importance in the mathematical analysis for the derivation of a priori estimates which are needed, for instance, in the existence and longtime analysis. Numerical schemes should be designed in such a way that the structural features are preserved on the discrete level in order to obtain accurate and stable algorithms. Whereas consistency and stability of numerical schemes have received much attention in the literature, much less is known about structure-preserving schemes. In this project, we wish to explore the entropy structure of certain highly nonlinear parabolic equations and their systems and to derive new structure-preserving numerical schemes. Equations considered in this project include second-order (porous-medium) equations, fourth-order (thin-film, quantum diffusion or Derrida-Lebowitz-Speer-Spohn) equations, and Maxwell-Stefan systems for multicomponent gaseous mixtures.

Personen

Projektleiter_in

Institut

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Forschungsschwerpunkte

  • Mathematical and Algorithmic Foundations: 100%

Schlagwörter

DeutschEnglisch
EntropiemethodenEntropy methods
Nichtlineare EvolutionsgleichungenNonlinear evolution equations
Strukturerhaltende SchemataStructure-preserving schemes
Numerische ApproximationenNumerical approximations

Publikationen