ASSESSMENT OF CENTERED DIFFERENCE SCHEMES ACCURACY FOR DYNAMIC PROBLEMS OF ELASTICITY THEORY IN INTERPOLATION SPACES

In the present paper, we investigate the accuracy of difference schemes for the first-order hyperbolic systems for the case of two-dimensional equations of dynamical theory of elasticity under weak smoothness assumptions on the solutions of the differential problem. Developing the apparatus of stability theory of difference schemes, we obtain an a priori error bound in a norm weaker than. Using this bound and the Bramble-Hilbert lemma, to estimate the approximation error, we prove O(τ^m + h^m) convergence of the scheme to the solution of the differential problem from the class W_2^m (Q_T ), m = 1, 2. Besides, we obtained the accuracy of bounds in the interpolations space.