On accuracy and performance of high-order finite volume methods in local mean energy model of non-thermal plasmas

In this paper, a high-order finite volume method is employed to solve the local energy approximation model equations for a radio-frequency plasma discharge in a one-dimensional geometry. The so called deferred correction technique, along with high-order Lagrange polynomials, is used to calculate the convection and diffusion fluxes. Temporal discretization is performed using backward difference schemes of first and second orders. Extensive numerical experiments are carried out to evaluate the order and level of accuracy as well as computational efficiency of the various methods implemented in the work. These tests exhibit global convergence rate of up to fourth order for the spatial error, and of up to second order for the temporal error.