On one modification of Marchuk-Kuzin's scheme for parabolic equations with mixed derivatives

In the article, we propose and study one modification of the finite element splitting algorithm for the solution to the Neumann boundary parabolic problem with mixed derivatives. We consider the simplest equations with constant coefficients without advective terms. In our case, for the Neumann problem, the error estimate contains the term O(τ√h), and the numerical experiments show that this estimate cannot be improved. We give the modification with the estimate O(τ+h). The approach is based on our results for the parabolic problems in nonrectangular domains.