On convergence of schemes of finite element method of high accuracy for the equation of heat and moisture transfer

Abstract

In this paper difference schemes of the finite element method of a high order of accuracy for the nonstationary equation of moisture transfer of Aller are constructed and investigated. The increased order of accuracy is achieved through special sampling of temporal and spatial variables. The stability and convergence of the constructed numerical algorithms are proved, the corresponding a priori estimates are obtained in various norms, which are used later to obtain estimates of the accuracy of the scheme under weak assumptions on the smoothness of solutions to the differential problem.