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

Dennis E. Jackson

 Florida Institute of Technology, Department of Applied Mathematics, 150 W. University Blvd., Melbourne 32901, FL, USA
Received 1 February 1991; Revised 1 April 1991

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.