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Title:
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A mixed finite element method for nonlinear diffusion equations
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Author:
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Burger, Martin; Carrillo, José A.; Wolfram, Marie-Therese
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Other authors:
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Centre de Recerca Matemàtica |
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Resum:
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We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation.
This formulation preserves the maximum principle in case of the semi-discrete
scheme as well as the fully discrete scheme for a certain class of problems.
In addition solutions of the mixed formulation maintain exponential convergence
in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. |
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Publication date:
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2009-10 |
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Subject (UDC):
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517 - Anàlisi |
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Subject(s):
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Teories no-lineals
Elements finits, Mètode dels |
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Rights:
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Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
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Document type:
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Preprint |
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