The Lagrange-Euler method for the numerical solution of multidimensional problems of convective diffusion. (Q2754699)

As a sample problem, the first boundary-value problem for the equation of convective diffusion in a rectangle is considered. Advantages and disadvantages of known numerical schemes of solution are discussed. For the approximation of equations of convective transport, the combined Lagrange-Euler method is suggested. Details of grid formation and derivatives approximation are explained. The error introduced by the numerical scheme is investigated. A theorem that the suggested scheme is uniformly converging when both temporal and spatial steps of discretization independently tend to zero and that this scheme has first order accuracy is proved. Comparison of a test example with the analytic solution for an infinite domain is done. Isolines of mean-square error are presented.