A stabilized finite element method for modeling of gas discharges

An efficient stabilized finite element method for modeling of gas discharge plasmas is represented which provides wiggle-free solutions without introducing much artificial diffusion. The stabilization is achieved by modifying the standard Galerkin test functions by means of a weighted quadratic term that results in a consistent Petrov–Galerkin formulation of the charge carriers in the plasma. Using the example of a glow discharge plasma in argon, it is shown that this efficient method provides more accurate results on the same spatial grid than the widely used finite difference approach proposed by Scharfetter–Gummel if the weighting factor is determined in dependence on the local Péclet number and the modified test functions are consistently applied to all terms of the governing equations.