Convergence of Fourth Order Compact Difference Schemes for Three-Dimensional Convection-Diffusion Equations

Authors:
Givi Berikelashvili;Murli M. Gupta;Manana Mirianashvili
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 5

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Abstract

We consider a Dirichlet boundary-value problem for the three-dimensional convection-diffusion 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 $W_2^m(\omega)$-norm with the convergence rate $O(h^{s-m})$, where the real parameter $s$ satisfies the condition $\max (1.5, m)