Efficient, accurate and flexible finite element solvers for chemotaxis problems

Authors:
Robert Strehl;Andriy Sokolov;Stefan Turek
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2012

Citing 4
Cited 2

A finite volume scheme for the Patlak–Keller–Segel chemotaxis model

Numerische Mathematik
Discontinuous Galerkin methods for the chemotaxis and haptotaxis models

Journal of Computational and Applied Mathematics
A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

Numerische Mathematik
New Interior Penalty Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model

SIAM Journal on Numerical Analysis

Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection-diffusion equations on triangular meshes

Journal of Computational Physics
Nonnegativity of exact and numerical solutions of some chemotactic models

Computers & Mathematics with Applications

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Abstract

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.