Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method

Superconvergence analysis for a nonlinear parabolic equation is studied with a linearized 2-step backward differential formula (BDF) Galerkin finite element method (FEM). The error between the exact solution and the numerical solution is split into two parts by a time-discrete system. The temporal error estimates in -norm with order and in -norm with order are derived, respectively. The spatial error estimates are deduced unconditionally and the results help to bound the numerical solution in -norm. By some new way, the unconditional superclose property of in -norm with order is obtained. Two numerical examples show the validity of the theoretical analysis. Here, h is the subdivision parameter, and tau, time step size.