  The maximal regularity property of discontinuous Galerkin methods for linear
parabolic equations is used together with variational techniques to establish a
priori and a posteriori error estimates of optimal order under optimal
regularity assumptions. The analysis is set in the maximal regularity framework
of UMD Banach spaces. Similar results were proved in an earlier work, based on
the consistency analysis of Radau IIA methods. The present error analysis,
which is based on variational techniques, is of independent interest, but the
main motivation is that it extends to nonlinear parabolic equations; in
contrast to the earlier work. Both autonomous and nonautonomous linear
equations are considered.
