A p-adaptive, implicit-explicit mixed finite element method for diffusion-reaction problems

Wakeni, M. F. , Aggarwal, A. , Kaczmarczyk, Ł. , McBride, A. T. , Athanasiadis, I., Pearce, C. J. and Steinmann, P. (2022) A p-adaptive, implicit-explicit mixed finite element method for diffusion-reaction problems. International Journal for Numerical Methods in Engineering, 123(14), pp. 3237-3263. (doi: 10.1002/nme.6967)

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A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct a conforming base for the flux vectors, and a non-conforming base for the mass concentration of the species. The mixed formulation captures the distinct nonlinearities associated with the flux constitutive equations and the reaction terms. The IMEX method conveniently treats these two sources of nonlinearity implicitly and explicitly, respectively, within a single time-stepping framework. A reliable a posteriori error estimate is proposed and analyzed. A p-adaptive algorithm based on the proposed a posteriori error estimate is also constructed. The combination of the proposed residual-based a posteriori error estimate and hierarchical finite element spaces allows for the formulation of an efficient p-adaptive algorithm. A series of numerical examples demonstrate the performance of the approach for problems involving travelling waves, and possessing discontinuities and singularities. The flexibility of the formulation is illustrated via selected applications in pattern formation and electrophysiology.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Athanasiadis, Dr Ignatios and McBride, Professor Andrew and Wakeni, Dr Mebratu and Kaczmarczyk, Professor Lukasz and Steinmann, Professor Paul and Pearce, Professor Chris and Aggarwal, Dr Ankush
Authors: Wakeni, M. F., Aggarwal, A., Kaczmarczyk, Ł., McBride, A. T., Athanasiadis, I., Pearce, C. J., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal for Numerical Methods in Engineering
ISSN (Online):1097-0207
Published Online:10 March 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in International Journal for Numerical Methods in Engineering 123(14): 3237-3263
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300129Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational MechanicsChristopher PearceEngineering and Physical Sciences Research Council (EPSRC)EP/R008531/1ENG - Infrastructure & Environment