Convergence of the Galyorkin method of approximate solving of parabolic equation with weight integral condition on a solution

In the Hilbert space the abstract linear parabolic equation with nonlocal weight integral condition is resolved approximately by Galyorkin method. Estimates on projection subspaces are oriented on the finite element method. We consider the case of projection subspaces built by the uniform partition of domain of variation of space variables and also the case of arbitrary projection subspaces of the type of finite elements. We obtain the errors estimations of approximate solutions and establish the orders of rate of convergence exact by order of approximation.