Wavelet-based Discrete-continual Finite Element Method of Local Structural Analysis for Two-dimensional Problems

High-accuracy solution in structural analysis is normally required in some pre-known domains (regions of structure with the risk of significant stresses that could potentially lead to the destruction, regions subjected to specific operational requirements). This paper is devoted to wavelet-based discrete-continual finite element method (DCFEM) of local analysis of deep beams with piecewise constant physical and geometrical parameters in so-called “basic” direction. Initial discrete-continual operational formulation and corresponding formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem for system of ordinary differential equations is given.