Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 1, Pages 19-27
doi:10.1155/S1048953392000029
Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations
Florida Institute of Technology, Department of Applied Mathematics, 150 W. University Blvd., Melbourne 32901, FL, USA
Received 1 February 1991; Revised 1 April 1991
Copyright © 1992 Dennis E. Jackson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Existence and uniqueness are proved for nonlocal (in time) for
solutions of linear parabolic partial differential equations. Instead of an
initial condition, there is a relation connecting the initial value to values
of the solution at other times. L2 error estimates are obtained for the
semidiscrete approximation of the problem using finite elements in the
space variables.