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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Wiley
• ISSN: 0029-5981
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300129		Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics	Christopher Pearce	Engineering and Physical Sciences Research Council (EPSRC)	EP/R008531/1	ENG - Infrastructure & Environment