EAPs (electro-active polymers) are becoming increasingly used as actuators, sensors, and energy harvesters. Finite element simulations are proven to be an indispensable tool for simulating the complicated behaviour of actuators under coupled loads, especially in the fields of soft robotics, biomedical engineering, and energy harvesting. We provide a new finite element framework for simulating coupled static and dynamic electromechanical interactions in electro active polymeric materials in this paper. A two-field mixed displacement-pressure formulation is used to mimic the incompressible character of EAPs, which, unlike the commonly used mixed three-field and F-bar formulas, is applicable for both virtually and fully incompressible materials. Innovative quadratic Bezier triangular and tetrahedral elements are employed for spatial discretization. A monolithic scheme is used to solve the governing equations for the coupled electromechanical issue; for electrodynamics simulations, a state-of-the-art implicit time integration is adapted. Several benchmark examples in computational electro mechanics, such as simulations of a spherical gripper in electrostatics and a dielectric pump in electrodynamics, are used to show the accuracy and computing efficiency of the proposed framework.