A meshless method for the Cauchy problem in linear elastodynamics

In this paper, we establish new density result for the Navier equation. Based on the denseness of the elastic single-layer potential functions, the Cauchy problem for the Navier equation is investigated. The ill-posedness of this problem is given via the compactness of the operator defined by the potential function. The method combines the Newton's method and minimum norm solution with discrepancy principle to solve an inverse problem. Convergence and stability estimates are then given with some examples for numerical verification on the efficiency of the proposed method.