On one type of finite element simulation in dynamic elasticity

The aim of the present paper is to generalize the finite element approximation for numerical simulation of special types of problems in the dynamic theory of elasticity, described by the two-dimensional mixed boundary value problems, and to demonstrate the property of their numerical solution. Physically the problems describe propagation of elastic waves, generated by a harmonic line source, in a nonhomogeneous anisotropic media. The existence and unicity of the weak solution as well as of the finite element approximation is proved. Convergence of the method is proved for any regular family of triangulations.