Optimal convergence rates for semidiscrete approximations of parabolic problems with nonsmooth boundary data
Gilbert Choudury, Irena Lasiecka · Numerical Functional Analysis and Optimization · 1991
We consider semidiscrete approximations of parabolic boundary value problems based on an elliptic approximation by J. Nitsche, in which the approximating subspaces are not subject to any boundary conditions. Optimal Lp (L 2) error estimates are derived for both smooth and nonsmooth boundary data. The approach is based on semigroup theory combined with the theory of singular integrals.