Convergence of High-Precision Finite Element Method Schemes for Two-Temperature Plasma Equation

In this paper, difference schemes of the high-order finite element method for the Sobolev type equation are constructed and investigated. In particular, boundary value problems for the two-temperature plasma equation are considered. A high order of accuracy of the scheme is achieved by special sampling of time and space variables. The stability and convergence of the constructed algorithms are proved. A priori estimates are obtained in various norms, which are used later to obtain estimates of the accuracy of the scheme under weak assumptions about the smoothness of solutions to differential problems.