The accurate calculation of the electrostatic forces between charged particles requires a reliable representation of the emerging electric field. To this end, two principle formulations are available, namely Coulomb's and Gauss' laws. While both approaches are in this specific case mathematically equivalent, the numerical solution of Gauss' law on a grid is contaminated by a spatial discretization error. In this paper, we explore under which conditions this error depreciates the computed results of the particle dynamics. More specifically, we introduce a length-scale of the electrostatic interaction which serves as a base to evaluate the required grid resolution. Also, according to our numerical study, this error reduces in case the particle dynamics is contact dominated. Furthermore, we introduce a computationally efficient hybrid scheme which combines the advantages of both formulations and examine in which situations its accuracy is superior to schemes based on the numerical solution of Gauss' law. (C) 2017 Elsevier B.V. All rights reserved.