Galerkin Methods for Vibration Problems in Two Space Variables

Abstract

Some discrete Galerkin methods are formulated for approximately solving a linear fourth order parabolic partial differential equation in $\Omega \times (0,T]$, where $\Omega $ is an arbitrary bounded domain in $\mathbb{R}^2 $. Error estimates are obtained which show that these methods are second order correct in time. When $\Omega $ is a rectangle, alternating-direction Galerkin methods are discussed.