Fully discrete approximations of parabolic boundary-value problems with nonsmooth boundary data

We study a numerical scheme for the approximation of parabolic boundary-value problems with nonsmooth boundary data. This fully discrete scheme requires no boundary constraints on the approximating elements. Our principal result is the derivation of optimal convergence estimates in L_p0,T; L₂()] norms for boundary data in L_p0, T; L₂()], 1p . For the same algorithms, we also show that the convergence remains optimal even in higher norms. The techniques employed are based on the theory of analytic semigroups combined with singular integrals.This paper was written in 1990, when the author was in the Department of Mathematical Sciences, University of Cincinnati. A preliminary version of this research was presented at the SIAM Annual Meeting in July 1989.