Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

Abstract

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The $L^2$ norm and $H^1$ semi-norm error estimates are obtained for the first scheme and the second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.