Galerkin methods for parabolic equations with nonlinear boundary conditions

Abstract

A variety of Galerkin methods are studied for the parabolic equationu t =??(a(x)? u),x?Ω?? n ,t? (O,T], subject to the nonlinear boundary conditionu v =g(x,t,u),x??Ω,t? (O,T] and the usual initial condition. Optimal order error estimates are derived both inL 2 (Ω) andH 1 (Ω) norms for all methods treated, including several that produce linear computational procedures.