Comparison of Solutions of the Problems of Elasticity Theory for Different Near-Boundary Elements

We consider three types of near-boundary elements: curvilinear quadrangles and families of arcs and points, and their application to a two-dimensional problem of the static theory of elasticity with boundary conditions in displacements. The comparison of the theoretical and numerical aspects of the obtained solutions is performed. It is shown that the accuracy of evaluation of the components of the vector of displacements increases in the following cases: in the case of complete quantization of the near-boundary region (but not in the case of its partial quantization or quantization with overlapping), in the case where the numbers of arcs and points increase, and in the case of simultaneous application of different types of near-boundary elements (specifically, quadrangles and families of arcs).