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Summary: A POSTERIORI ERROR ESTIMATION FOR THE
FINITE ELEMENT METHOD-OF-LINES SOLUTION
OF PARABOLIC PROBLEMS
SLIMANE ADJERID and JOSEPH E. FLAHERTY
Department of Computer Science and Scienti c Computation Research Center
Rensselaer Polytechnic Institute, Troy, NY 12180, USAadjerids@cs.rpi.edu, aherje@cs.rpi.edu
IVO BABUSKA
Texas Institute for Computational and Applied Mathemathics
University of Texas at Austin, Austin, TX 78712
Abstract
Babuska and Yu constructed a posteriori estimates for nite element dis-
cretization errors of linear elliptic problems utilizing a dichotomy principal
stating that the errors of odd-order approximations arise near element edges
as mesh spacing decreases while those of even-order approximations arise in
element interiors. We construct similar a posteriori estimates for the spatial
errors of nite element method-of-lines solutions of linear parabolic partial
di erential equations on square-element meshes. Error estimates computed in
this manner are proven to be asymptotically correct; thus, they converge in
strain energy under mesh re nement at the same rate as the actual errors.
1. Introduction
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