CONVERGENCE OF FOURTH ORDER COMPACT DIFFERENCE SCHEMES FOR THREE-DIMENSIONAL CONVECTION-DIFFUSION EQUATIONS

摘要

We consider a Dirichlet boundary-value problem for the three-dimensional convectiondiffusion equations with constant coefficients in the unit cube. A high order compact finite difference scheme is constructed on a 19-point stencil using the Steklov averaging operators. We prove that the finite difference scheme converges in discrete W_2~m (ω)-norm with the convergence rate O(h~(s-m)),where the real parameter s satisfies the condition max(1.5,m) < s ≤ m + 4, m = 0, 1, 2, and the exact solution belongs to the Sobolev space W_2~s (Ω).