Discrete time Galerkin methods for a parabolic boundary value problem

Abstract

Single step discrete time Galerkin methods for the mixed initial-boundary value problem for the heat equation are studied. Two general theories leading to error estimates are developed. Among the examples analyzed in the application of these theories are methods in which the related quadratic form is required to be definite only on the subspace of approximating functions and two classes containing methods of arbitrary given order of accuracy, one requiring satisfaction of certain boundary conditions by the elements of the subspace, the other making no such requirements. © 1974 Fondazione Annali di Matematica Pura ed Applicata.