A mixed finite element method for nonlinear diffusion equations
Burger, Martin (Institut für Numerische und Angewandte Mathematik (Munster, Alemanya))
Carrillo de la Plata, José Antonio (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Wolfram, Marie-Therese (University of Cambridge. Department of Applied Mathematics and Theoretical Physics)
Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Imprint: Centre de Recerca Matemàtica 2009
Description: 26 p.
Abstract: 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.
Rights: 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 Creative Commons
Language: Anglès
Series: Centre de Recerca Matemàtica. Prepublicacions
Series: Prepublicacions del Centre de Recerca Matemàtica ; 891
Document: article ; submittedVersion
Subject: Teories no-lineals ; Elements finits, Mètode dels

Adreça alternativa: https://hdl.handle.net/2072/46799


26 p, 1.1 MB

The record appears in these collections:
Research literature > Preprints

 Record created 2010-04-14, last modified 2020-11-19



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