Journal of Computational Physics 148, 605–620 (1999) Article ID jcph.1998.6132, available online at http://www.idealibrary.com on An Improved Finite-Element Flux-Corrected Transport Algorithm G. E. Georghiou, ∗ R. Morrow,† and A. C. Metaxas ∗ ∗ Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom; †CSIRO, Division of Telecommunications and Industrial Physics, Bradfield Road, West Lindfield, P.O. Box 218, Lindfield NSW 2070, Australia E-mail: geg1000@eng.cam.ac.uk, acm@eng.cam.ac.uk, richard.morrow@tip.csiro.au Received February 3, 1998; revised October 15, 1998 An improved finite-element flux-corrected transport (FE-FCT) method for the nu- merical solution of hydrodynamic conservation equations is described, based on the method developed by Lohner and his collaborators to solve conservation equations in fluid mechanics, and its application is extended to gas discharge problems. The high- and low-order schemes used are the ones proposed by Lohner who adds dif- fusion to the high-order scheme by subtracting the lumped-mass matrix from the consistent-mass matrix to give the low-order scheme; the diffusion coefficient is adjusted globally. A variable diffusion coefficient is introduced; it is assumed to be constant in each element and is shown to transform the high-order solution to a scheme equivalent to an upwind scheme which has minimal diffusion but en- sures positive results. This avoids the complexity of upwinding in FE, especially in two dimensions. It is also shown that the correct amount of “real” diffusion may be easily added to the algorithm when required, for example, for electrons. Re- sults are presented which show that the high-order scheme reduces to the upwind difference scheme when the new diffusion is used. The proposed FCT scheme is shown to give similar results, in comparison with a fourth-order FD-FCT algorithm. Finally, the new method is applied to a streamer propagation problem in one dimen- sion, and the results obtained are shown to agree well with previously published results. c  1999 Academic Press Key Words: flux-corrected transport; conservation equations; streamers; gas dis- charges; Poisson’s equation. 1. INTRODUCTION Equations describing the drift and diffusion of charged particles in an electric field rep- resent the starting point for most theoretical studies in gaseous discharges. In many cases the electric field, being controlled by space-charge effects, must be obtained from Poisson’s 605 0021-9991/99 $30.00 Copyright c  1999 by Academic Press All rights of reproduction in any form reserved.