Error estimates for the numerical solution of a time-periodic linear parabolic problem

In this paper we consider the numerical solution of a time-periodic linear parabolic problem. We derive optimal order error estimates inL₂() for approximate solutions obtained by discretizing in space by a Galerkin finite-element method and in time by single-step finite difference methods, using known estimates for the associated initial value problem. We generalize this approach and obtain error estimates for more general discretization methods in the norm of a Banach spaceB L₂(), e.g.,B=H₀¹() orL(). Finally, we consider some computational aspects and give a numerical example.