Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations
Tongke Wang 1*1 School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China.
Received 30 September 2009; Accepted (in revised version) 18 March 2010
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 second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.AMS subject classifications: 65M08, 65M12, 65M15
Key words: Three-dimensional parabolic equation, alternating direction method, finite volume element method, error estimate.
Email: email@example.com (T. Wang)