Assessment of centered difference schemes accuracy for dynamic problems of elasticity theory in interpolation spacesD. Utebae (pp. 176-181)
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 convergence of the scheme to the solution of the differential problem from the class. Besides, we obtained the accuracy of bounds in the interpolations space.
equation dynamic elasticity theory, ¯nite di®erence method, approximation, stabi- lity, convergence, interpolation space.