Superconvergence of the Gradient in Piecewise Linear Finite-Element Approximation to a Parabolic Problem

Some recent results concerning maximum-norm superconvergence of the gradient in piecewise linear finite-element approximations of an elliptic problem are carried over to a parabolic problem. Both the standard semidiscrete in space Galerkin method and the lumped mass modification are analyzed for both smooth and nonsmooth data situations, and the Crank–Nicolson discretizations in time of these procedures are considered as examples of completely discrete schemes.