Estimates for errors in two-dimensional models of elasticity theory (Q2773605)

The author exposes a method for studying a three-dimensional variational problem of elasticity theory by means of reduction of the dimension of the problem. This approach is based on using error estimates of solutions to the reduced problem from an exact solution to the original problem and is applied in the case when one of the characteristic sizes of the domain is essentially less than the others.NEWLINENEWLINE The main aim of the article is to obtain an a posteriori error estimate for solutions to the problem. First, the author presents a general form of an error estimate for solutions to an abstract variational problem with quadratic functional. Then, he employes the results obtained to the three-dimensional problem under consideration. Finally, error estimates are given for solutions to the two-dimensional problem. The error estimates obtained are written in an explicit form.