On the Combination of Finite Element and SplittingUp Methods in the Solution of Parabolic Equations
Abstract
A scheme combining finite element and splittingup methods is suggested for the numerical solution of a parabolic equation in two dimensions. Approximation in space variables is implemented by the finite element method on a rectangular grid, triangulated by the diagonals. A finitedifference operator of the problem is split into four positive semidefinite onedimensional operators acting along coordinate and diagonal directions. For the integration with respect to time, a twocycle splittingup scheme of the solution is used. The application of the method to a nonuniform grid topologically equivalent to a rectangular one is studied, and the stability conditions of the splittingup method in this case are obtained.
 Publication:

Journal of Computational Physics
 Pub Date:
 November 1983
 DOI:
 10.1016/00219991(83)90030X
 Bibcode:
 1983JCoPh..52..237M