A time-stepping method for Galerkin approximations for nonlinear parabolic equations

A modified backward difference time discretization is considered for Galerkin approximations to the solution of the nonlinear parabolic equation c(x, u)ut−▽·(a(x, u)▽u)=f(x, u). This procedure allows efficient use of such direct methods for solving linear algebraic equations as nested dissection. Optimal order error estimates and almost optimal order work requirements are derived.