Galerkin Finite Element Methods for Parabolic Problems

The standard Galerkin method.- Semidiscrete methods based on more general approximations of the elliptic problem.- Smooth and non-smooth data error estimates for the homogeneous equation.- Parabolic equations with more general elliptic operators.- Maximum-Norm estimates.- Negative norm estimates and superconvergence.- Completely discrete schemes for the homogeneous equation.- Completely discrete schemes for the inhomogeneous equation.- Time discretization by the discontinuous Galerkin method.- A nonlinear problem.- The method of lumped masses.- The H1 and H?1 methods.- A mixed method.- A singular problem.