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Ionomeric polymer–metal composites (IPMCs) consist of an ionomer with bound anionic groups and mobile counterions. They are plated with noble impermeable metal cover layers. By application of an electric voltage, a transport of the mobile ions towards the respective electrode occurs. Due to local electrostatic and ionic forces, a local deformation of the IPMC can be observed. Therefore IPMCs are promising candidates for electrochemical transducers. In the present research, the chemo-electro-mechanical behavior of IPMCs is described within the framework of the theory of porous media. First, the field equations are derived with respect to the second law of thermodynamics. Second, a reduced set of equations for the chemo-electric behavior is formulated and discretized by applying the finite element method. In the numerical investigations a parametric study of the time and space dependent behavior is carried out in order to quantify the influence of different material compositions. Based on this study, the characteristic response of IPMC to the application of an electric voltage can be predicted. Concluding, the obtained computational framework is an excellent tool for the design of electrochemical transducers.

In the present contribution we propose an improved mixed least-squares finite element method (LSFEM) and compare it with standard LSFEMs with respect to performance aspects. In detail, we consider an approach for Newtonian fluid flow, which is described by the incompressible Navier-Stokes equations. The basis for the associated symmetric minimization problem is a reduced stress-velocity (s-v) two-field approach, see e.g. CAI ET AL.[1] and SCHWARZ & SCHRÖDER [2]. The main idea for the proposed formulation is to add an additional equation, which yields an overconstrained first-order system. This approach does not introduce additional unknowns, so the advantage of two variables (stresses and velocities) remains. Finally, we present a numerical example in order to show the capability of the proposed formulation.

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The focus of this contribution is the examination of the influence of different interpolation orders (especially for the pressure field) by solving the stationary incompressible Navier‐Stokes equations with least‐squares finite elements. We consider two different div‐grad first‐order systems which result in a three‐field formulation with stresses, velocitites and pressure, see e.g. SCHWARZ & SCHRÖDER [1] and BOCHEV & GUNZBURGER [2]. Additionally, a numerical example is presented to show the performance of the considered formulations. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)