Abstract
This paper considers a difference scheme for solving the plane problem of the static theory of elasticity with non-homogeneous data in an arbitrary domain in the case where the tension at the boundary is given (second boundary value problem). The difference scheme is obtained from a variational principle with subsequent use of the generalized Ritz method with functions which are linear in each of the triangles of a rectangular net [1, 2]. The scheme obtained approximates the differential equation to the second order at ‘internal’ points, and the boundary conditions are approximated to at least the first order of approximation, if the solution is sufficiently smooth. It is proved that a solution of the difference problem exists for a function which is a linear completion of the solution of the difference problem, a prior estimate is obtained in the metric W 2 (1), it is proved that this linearly completed function converges to the solution at a rate O( h 1 + h 2), if the solution belongs to W 2 (2), and a stable method of solving the difference equation is indicated.
Published Version
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