An embodiment of the invention involves increasing the penalty stiffness within a finite element simulation increment, which is more accurate because it avoids following a solution path with significant non-physical penetrations. An embodiment of the present invention begins by determining a first value of a parameter used by a finite element simulation of a load increment. Next, a first solution of the finite element simulation is determined by performing Newton iterations using the first value of the parameter until a first convergence check is satisfied. Then, a second value the parameter is determined wherein the second value of the parameter is unequal to the first value of the parameter. Finally, a second solution of the finite element simulation is determined by continuing the Newton iterations using the second value of the parameter until a second convergence check is satisfied, the first convergence check being different than the second convergence check.