Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 64, Issue 3, Pages 175-189Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2011.12.040
Keywords
Chemotaxis model; Pattern formation; Finite element; Newton; Monolithic; Nonlinear
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In the framework of finite element discretizations, we introduce a fully nonlinear Newton-like method and a linearized second order approach in time applied to certain partial differential equations for chemotactic processes incorporating two entities, a chemical agent and the reacting population of certain biological organisms/species. We investigate the benefit of a corresponding monolithic approach and the decoupled variant. In particular, we analyze accuracy, efficiency and stability of different methods and their dependences on certain parameters in order to identify a well suited finite element solver for chemotaxis problems. (C) 2011 Elsevier Ltd. All rights reserved.
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