 
Summary: A POSTERIORI ERROR ESTIMATION FOR THE
FINITE ELEMENT METHODOFLINES 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 oddorder approximations arise near element edges
as mesh spacing decreases while those of evenorder approximations arise in
element interiors. We construct similar a posteriori estimates for the spatial
errors of nite element methodoflines solutions of linear parabolic partial
di erential equations on squareelement 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
