Commun. Comput. Phys., 11 (2012), pp. 249-270.


Modeling Ionic Polymer-Metal Composites with Space-Time Adaptive Multimesh hp-FEM

David Pugal 1, Pavel Solin 2*, Kwang J. Kim 3, Alvo Aabloo 4

1 Mechanical Engineering Department, University of Nevada, Reno Reno, NV 89557, USA; and Institute of Technology, University of Tartu, Nooruse St 1, 50411 Tartu, Estonia.
2 Department of Mathematics and Statistics, University of Nevada, Reno Reno, NV 89557, USA; and Institute of Thermomechanics, Prague, Czech Republic.
3 Mechanical Engineering Department, University of Nevada, Reno Reno, NV 89557, USA.
4 Institute of Technology, University of Tartu, Nooruse St 1, 50411 Tartu, Estonia.

Received 8 November 2010; Accepted (in revised version) 18 March 2011
Available online 8 September 2011
doi:10.4208/cicp.081110.180311a

Abstract

We are concerned with a model of ionic polymer-metal composite (IPMC) materials that consists of a coupled system of the Poisson and Nernst-Planck equations, discretized by means of the finite element method (FEM). We show that due to the transient character of the problem it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time. We also show that due to large qualitative and quantitative differences between the two solution components, it is efficient to approximate them on different meshes using a novel adaptive multimesh hp-FEM. The study is accompanied with numerous computations and comparisons of the adaptive multimesh hp-FEM with several other adaptive FEM algorithms.

AMS subject classifications: 35Q99, 65M50, 65M60, 65H10, 65M22
PACS: 02.70.Dh, 41.20.Cv, 66.30.Qa
Key words: Ionic polymer-metal composites, IPMC, Nernst-Planck equation, Poisson equation, finite element method, FEM, adaptive multi-mesh hp-FEM.

*Corresponding author.
Email: david.pugal@gmail.com (D. Pugal), solin@unr.edu (P. Solin), kwangkim@unr.edu (K. Kim), alvo@ut.ee (A. Aabloo)
 

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