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An energy-based model of the ferroelectric polarization process is presentedin the current contribution. In an energy-based setting, dielectricdisplacement and strain (or displacement) are the primary independent unknowns.As an internal variable, the remanent polarization vector is chosen. The modelis then governed by two constitutive functions: the free energy function andthe dissipation function. Choices for both functions are given. As thedissipation function for rate-independent response is non-differentiable, it isproposed to regularize the problem. Then, a variational equation can be posed,which is subsequently discretized using conforming finite elements for eachquantity. We point out which kind of continuity is needed for each field(displacement, dielectric displacement and remanent polarization) is necessaryto obtain a conforming method, and provide corresponding finite elements. Theelements are chosen such that Gauss' law of zero charges is satisfied exactly.The discretized variational equations are solved for all unknowns at once in asingle Newton iteration. We present numerical examples gained in the opensource software package Netgen/NGSolve.

High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials