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

Abstract

In this paper we consider the numerical solution of a time-periodic linear parabolic problem. We derive optimal order error estimates inL 2(Ω) 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 ⊂L 2(Ω), e.g.,B=H 0 1 (Ω) orL ∞(Ω). Finally, we consider some computational aspects and give a numerical example.