  We make progress towards a 3D finite-element model for the magnetization of a
high temperature superconductor (HTS): We suggest a method that takes into
account demagnetisation effects and flux creep, while it neglects the effects
associated with currents that are not perpendicular to the local magnetic
induction. We consider samples that are subjected to a uniform magnetic field
varying linearly with time. Their magnetization is calculated by means of a
weak formulation in the magnetostatic approximation of the Maxwell equations
(A-phi formulation). An implicit method is used for the temporal resolution
(Backward Euler scheme) and is solved in the open source solver GetDP. Picard
iterations are used to deal with the power law conductivity of HTS. The finite
element formulation is validated for an HTS tube with large pinning strength
through the comparison with results obtained with other well-established
methods. We show that carrying the calculations with a single time-step (as
opposed to many small time-steps) produce results with excellent accuracy in a
drastically reduced simulation time. The numerical method is extended to the
study of the trapped magnetization of cylinders that are drilled with different
arrays of columnar holes arranged parallel to the cylinder axis.
