Pointwise localized error estimates for parabolic finite element equations (Q1424371)

The semidiscretisation by a higher-order finite element method of the heat equation with homogeneous Neumann boundary is considered. The author proves pointwise weighted error estimates that extend results by \textit{A. H. Schatz} known for the corresponding stationary problem [Math. Comput. 67, No. 223, 877--899 (1998; Zbl 0905.65105)]. The estimates are more localized than the almost best approximation results in the maximum norm. The proof relies upon an approximation of Green's function.