Convergence rates of parabolic difference schemes for non-smooth data
Vidar Thomée, Lars B. Wahlbin · Mathematics of Computation · 1974
Consider the approximate solution of the initial-value problem for a parabolic system by means of a parabolic finite difference scheme of accuracy μ \mu . The main result of the present paper is essentially that for positive time and v in W 1 s {W_1}^s with 1 > s ≤ μ 1 > s \leq \mu , the error in the maximum norm is O ( h s ) O({h^s}) for small mesh-widths h .