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Improved Accuracy for Alternating-Direction Methods for Parabolic Equations Based on
 

Summary: Improved Accuracy for Alternating-Direction
Methods for Parabolic Equations Based on
Regular and Mixed Finite Elements
Todd Arbogast
, Chieh-Sen Huang
,,
Song-Ming Yang
.
November 22, 2005
Abstract
An efficient modification by Douglas and Kim of the usual alternating directions
method reduces the splitting error from O(k2
) to O(k3
) in time step k. We prove conver-
gence of this modified alternating directions procedure, for the usual non-mixed Galerkin
finite element and finite difference cases, under the restriction that k/h2
is sufficiently
small, where h is the grid spacing. This improves the results of Douglas and Gunn, who
require k/h4
to be sufficiently small, and Douglas and Kim, who require that the locally

  

Source: Arbogast, Todd - Center for Subsurface Modeling & Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics; Geosciences