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A Study on Mixed Finite Element Formulations Applied to Diffusion Problems
Author(s) -
Kaessmair Stefan,
Javili Ali,
Steinmann Paul
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410230
Subject(s) - finite element method , diffusion , mathematics , order (exchange) , mixed finite element method , diffusion equation , field (mathematics) , element (criminal law) , mathematical analysis , physics , thermodynamics , pure mathematics , engineering , metric (unit) , operations management , finance , political science , law , economics
The objective of this contribution is to study various mixed finite element schemes applied to classical and non‐classical diffusion problems. The Fickean diffusion is considered using a three‐field formulation where the concentration gradient and the diffusive flux are additionally chosen as independent variables. Furthermore, the non‐classical diffusion model given by the Cahn–Hilliard equation is discussed where mixed finite elements are used to cast the fourth‐order PDE into two second‐order PDEs. A penalized version of a mixed formulation for the underlying second gradient model is given by specific micromorphic models. Another approach is a classical second order splitting method. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)