On the convergence and rate of the convergence of a projection-difference method for approximate solving a parabolic equation with weight integral condition

In the Hilbert space the abstract linear parabolic equation with nonlocal weight integral condition for the solution is resolved approximately by projection-difference method using time-implicit Euler’s method. Approximation of the problem by spatial variables is oriented on the finite element method. Errors estimations of approximate solutions, convergence of approximate solution to exact one and orders of rate of convergence are established.