A PRIORI L~2 ERROR ESTIMATES FOR GALERKIN METHODS FOR NONLINEAR SOBOLEV EQUATIONS

摘要

In this paper we study Galerkin approximations to the solution of the nonlinearSobolev equation c(u)u_t=▽·{a(u)▽u_t+b(u)▽u}+f(u)in two spatial dimensions and deriveoptimal L~2 error estimates for the continuous-time,Crank-Nicolson and extrapolated Crank-Nicolson discrete-time approximations.