Implicit finite element discretizations based on the flux‐corrected transport algorithm

Abstract

AbstractThe flux‐corrected transport (FCT) methodology is generalized to implicit finite element schemes and applied to the Euler equations of gas dynamics. For scalar equations, a local extremum diminishing scheme is constructed by adding artificial diffusion so as to eliminate negative off‐diagonal entries from the high‐order transport operator. To obtain a nonoscillatory low‐order method in the case of hyperbolic systems, the artificial viscosity tensor is designed so that all off‐diagonal blocks of the discrete Jacobians are rendered positive semi‐definite. Compensating antidiffusion is applied within a fixed‐point defect correction loop so as to recover the high accuracy of the Galerkin discretization in regions of smooth solutions. All conservative matrix manipulations are performed edge‐by‐edge which leads to an efficient algorithm for the matrix assembly. Copyright © 2005 John Wiley & Sons, Ltd.