A 3-D transient finite element model is developed to represent the oscillating thermal convection induced in a simplified Bridgman configuration filled with a Ga-doped germanium melt in microgravity under the influence of an external magnetic field. The model development is based on the penalty-finite element solution of the equations describing the transport of momentum, heat and solution and also the electromagnetic field distribution in the melt pool. Automatic time step control is applied to help speed up the calculations. Numerical performance of finite element simulations for this class of problems is discussed. In particular, various types of finite element formulations were studied to minimize the global matrix size and to investigate the computational efficiency. Numerical simulations are conducted to study the convection and magnetic damping effects as a function of frequency, directions and amplitudes of g-jitter and also the direction and magnitudes of the applied magnetic fields. The results show that the g-jitter driven flow is time dependent and complex convection pattern can develop in a 3-D configuration even when the thermal conditions are symmetric and that the convection can be suppressed with an applied magnetic field.