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

摘要: 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 -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 are derived by applying the reconstruction technique.