Galerkin Finite Element Methods for Parabolic Problems.

The Standard Galerkin Method.- Methods Based on More General Approximations of the Elliptic Problem.- Nonsmooth Data Error Estimates.- More General Parabolic Equations.- Negative Norm Estimates and Superconvergence.- Maximum-Norm Estimates and Analytic Semigroups.- Single Step Fully Discrete Schemes for the Homogeneous Equation.- Single Step Fully Discrete Schemes for the Inhomogeneous Equation.- Single Step Methods and Rational Approximations of Semigroups.- Multistep Backward Difference Methods.- Incomplete Iterative Solution of the Algebraic Systems at the Time Levels.- The Discontinuous Galerkin Time Stepping Method.- A Nonlinear Problem.- Semilinear Parabolic Equations.- The Method of Lumped Masses.- The H1 and H?1 Methods.- A Mixed Method.- A Singular Problem.- Problems in Polygonal Domains.- Time Discretization by Laplace Transformation and Quadrature.