Solving Incorrect Problems of the Elasticity Theory

The possibilities of effective research and calculation of mathematical models described by problems with a unique solution on the subspace are substantiated by the example of the first main problem of the elasticity theory. A technique for obtaining a single solution of a variation problem on a subspace—a normal generalized solution—using a discrete finite element model on the entire space is proposed. The three-stage regularization method is used to find the normal generalized solution (or the weighted normal generalized solution) of the discrete problem—a system of linear algebraic equations with a symmetric semidefinite matrix. The three-stage regularization method allows us to approximate these solutions with a predetermined accuracy. This method is effectively implemented on modern high-performance computers.