Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations (Q1186522)

The author proves an existence and uniqueness result for a nonlocal (in time) parabolic equation. The nonlocality in time arises from the fact that instead of an initial condition there is a relation associating the initial value of the solution to values of the solution at other times. The author then considers a semidiscretization of the problem (using finite elements for the spatial discretization). He proves an existence and uniqueness result (for the semidiscrete problem) and derives an \(L^ 2\) estimate for the difference between the solution of the semidiscrete problem and the solution of the continuous problem.