A posteriori error estimates for fully discrete fractional-step $\vartheta$-approximations for the heat equation

Abstract

We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the discretization in space the finite element method with finite element spaces that are allowed to change with time. The first optimal order a posteriori error estimates in $L^{\infty }(0,T;L^2(\Omega ))$ are derived by applying the reconstruction technique.

22 pages, 6 figures

References in corpus (1)

• Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems