An improved adaptive remeshing process that allows the accurate control of the numerical solution of a partial differential 3D vectorial equation is introduced. It is applied to compute the electromagnetic intensity around a metallic sphere, which is known to present high gradients in limited zones of space. Thanks to the numerical results of an analytical model, we show that, the precision of the solution being controlled, this improved scheme permits to decrease drastically the computational time as well as the memory requirements by adapting the number and the position of nodes.