Confidence regions for solutions of applied boundary-value problems

We propose a practicable technique for determining the confidence regions of solutions of partial differential equations when errors are present both in the process of solution and in the process of specification (mathematical modeling) of the applied problem. The study focuses on applied boundary-value problems in the theory of shells. We elucidate the possibilities of determining the degree of confidence (both posterior and prior) of the numerical results depending on the use of various numerical schemes and mathematical models for some particular cases. Graphical and numerical data are presented demonstrating the application of the proposed technique.