New Hybrid-Streamline-Upwind Finite-Element Method in Dual Space : Fundamental Theory and Discrete Del Operator

Abstract

In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference analysis. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them accurately interpolates the functions appearing in convection-dominated flows, and the other becomes a hybrid-streamline-upwind weight function. Furthermore, we define a discrete del operator for the reduction of memory storage in computers. As a result, we achieve simplicity of formulation and high-speed calculation in the finite-element method.