Journal of Applied Mathematics and Stochastic Analysis
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.
Jackson, D.E. (1991) Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations. Journal of Applied Mathematics and Stochastic Analysis, 5(1), 19-27.