Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation

A novel technique is proposed for analyzing the convergence of a projection difference scheme as applied to the initial value problem for a quasilinear parabolic operator-differential equation with initial data u (0) a H. The technique is based on the smoothing property of solutions to the differential problem for t > 0. Under certain conditions on the nonlinear term, a new estimate of order O(root tau + h) for the convergence rate in a weighted energy norm is obtained without using a priori assumptions on the additional smoothness of weak solutions.