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 analytis 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 -- Multisteps 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
Summary
"This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis."--Jacket
Bibliography
Includes bibliographical references (pages 355-368) and index
