On the convergence of finite-difference schemes for parabolic equations with variable coefficients

Abstract

We study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW 2 1, 1/2 norm, compatible with the smoothness of generalized solutionu?W 2 ?, ?/2 (Q) (1<??3) and coefficients of equation.