The main focus of this work is to give an overview of the mathematical errors introduced by the temporal and spatial discretization in case of plasma simulations. Two standard models for the electric arc simulation have been used, for each of them a variation of the timestep and of the mesh density has been performed. Furthermore, three radiation models have been studied for each arc model in order to verify how this factor influences the overall computation stability. The results are analyzed and discussed by using standard methods developed for the quantification of the numerical uncertainty that appears in a simulation model. All the simulations have been performed with the commercial solver Ansys CFX.