The accuracy of approximations on rectangular grids in problems of the theory of elasticity with singularities
The asymptotic accuracy of a two-parameter family of difference schemes (including the finite-element method scheme with bilinear elements), which approximate mixed boundary-value problems on a regular rectangular grid in a half-plane for a system of equations of the linear theory of elasticity in which the first derivatives of the solutions have a singularity \(O (r^{- 1/2})\), is investigated. Integral representations of the grid solutions are found and their asymptotic series at infinity are obtained. The principal term of the error, of size \(O (h/r^{1/2})\), where \(r\) is the distance from the point where the type of boundary conditions changes, is computed.
two-parameter family of difference schemes
scientific article; zbMATH DE number 826009