Stokes 问题的一类有限体积元方法.pdfVIP

A Finite Volume Element Method for Stokes Problems Hongxing RUI School of Mathematics and System Science Shandong University Jinan 250100, China E-mail: hxrui@ Abstract: Consider the finite volume element method for the Stokes problem. We use a conforming piecewise linear function on a fine grid for velocity and piecewise constant element on a coarse grid for pressure. For general triangulation we prove the equivalence of the finite volume element method and a saddle-point problem, the inf-sup condition and the uniqueness of the approximation solution. We also give the optimal order H1 norm error estimate. For a widely used dual meshes we give the optimal L2 norm error estimates. Mathematics Subject classification (2000): 65N15, 65N30 Keyword: Finite volume element, Stokes problem, numerical analysis. 1 Introduction The finite volume element method(FVE) is a discretization technique for partial differ- ential equations, especially for those that arise from physical conservation laws including mass, momentum, and energy. FVE uses a volume integral formulation of the original problem and a finite partitioning set of covolumes to discretize the equation. The ap- proximate solution is chosen out of a finite element space [3], [6], [7], [15]. FVE is widely used in computational fluid mechanics and heat transfer problems [17]. It possesses the important and crucial property of inheriting the physical conservation laws of the original problem locally. Thus it can be expected to capture shocks, to produce simple stencils, or to study other physical phenomena more effectively