TY - JOUR T1 - Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 499 EP - 522 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.m99027 UR - https://global-sci.org/intro/article_detail/nmtma/6011.html KW - Three-dimensional parabolic equation, alternating direction method, finite volume element method, error estimate. AB -

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.