Galerkin Methods for Parabolic Equations

Abstract

Galerkin-type methods, both continuous and discrete in time, are considered for approximating solutions of linear and nonlinear parabolic problems. Bounds reducing the estimation of the error to questions in approximation theory are derived for the several methods studied. These methods include procedures that lead to linear algebraic equations even for strongly nonlinear problems. A number of computational questions related to these procedures are also discussed.