hp-FEM electromechanical transduction model of ionic polymer–metal composites

We propose a mathematically explicit model of ionic polymer–metal composite (IPMC) materials that consist of a coupled system of Poisson–Nernst–Planck–Euler equations, discretized by means of adaptive higher-order finite element methods (hp  -FEM). We show that due to the transient character of the problem and different fields in terms of the locations of field gradients in the domain 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 four solution components–cation concentration, electric potential, xx-directional displacement, and yy-directional displacement–it is efficient to approximate them on different meshes using a novel adaptive multi-mesh hp-FEM. The study is accompanied with computations and comparisons of the adaptive multi-mesh hp-FEM with a number of adaptive FEM algorithms.