Numerical Investigations of the Errors of the Bubnov–Galerkin Method

Abstract

In Chap. 3, many prior error estimates for the Bubnov–Galerkin method applied to coupled thermoelastic problems of shallow shells and plates were derived. The estimates related to the general case of a shell with a variable thickness subjected to time-varying mechanical and thermal loads possess an important theoretical meaning (they guarantee, for a wide class of problems, strong convergence of successive approximations to the exact solution with a velocity larger than the estimated velocity). However, in applications, when specific real problems have to be considered the estimates possess a more generalized meaning. This question is addressed, for instance, in the case of the estimates obtained in Sect. 3.3 for vibrations of a simply supported plate with constant thickness, subjected to mechanical and thermal loads that are constant in time. In this chapter, numerical results are given and the efficiency of the estimate used is verified.