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Discrete entropy structures in nonlinear diffusive evolution equations
01.04.2012 - 31.07.2016
Research funding project
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.
People
Project leader
Ansgar Jüngel
(E101)
Institute
E101 - Institute of Analysis and Scientific Computing
Grant funds
FWF - Österr. Wissenschaftsfonds (National)
Austrian Science Fund (FWF)
Research focus
Mathematical and Algorithmic Foundations: 100%
Keywords
German
English
Entropiemethoden
Entropy methods
Nichtlineare Evolutionsgleichungen
Nonlinear evolution equations
Strukturerhaltende Schemata
Structure-preserving schemes
Numerische Approximationen
Numerical approximations
Publications
Publications