Author(s)

M.A. Langerman & R.J. MacKinnon

Abstract

Application of compact high-order finite elements (CHOFE) to nonlinear convection-dominated problems M.A. Langerman" & R.J. MacKinnon^ "Mechanical Engineering Department, South Dakota School of Mines and Technology, Rapid City, SD, 57701, USA ^Nuclear Engineering Brookhaven National Laboratory, Upton, NY, 11973, USA A a new superconvergent, Petrov-Galerkin (PG), bilinear finite element method is presented for the solution of nonlinear convection-dominated problems. The scheme combines a generalized test function and artificial diffusion to achieve high-order [O(h )] grid-point accuracy. The solution is obtained on uniform (compact) stencils of 3x1 and 3x3 in one and two dimensions, respectively, without resorting to the extended stencils of high-order elements, thereby minimizing the matrix bandwidth. The CHOFE method is compared with the standard bilinear Galerkin finite-element method for convection-diffusion problems described by the steady form of the one- and t

Keywords