A selective enhanced FE-method for phase field modeling of ferroelectric materials

Ferroelectric materials are characterized by electrical di-poles, forming domains of uniform polarization orientation. In phase field models diffuse interfaces separate polarization domains as domain walls. Finite elements describe such interfaces with continuous field variables. But high gradients appear in the field variable requiring corresponding interpolations in the vicinity of domain walls. Otherwise, moving interfaces between phases stick to artificial minimum energy states, known as mesh-pinning. For this purpose, we study a selective enhancement of standard finite elements to avoid mesh-pinning effects. Our method enhances the ansatz space locally without impact on the physical theory or the overall finite element formulation.