ABSTRACT
This chapter explores the use of interval numbers to account for uncertainties in engineering models. We concentrate on models based on finite element discretization of partial differential equations. Results of such models are used ubiquitously in engineering design. Uncertainties in the results of finite element models can be attributed to the following sources:
1. The appropriateness of the partial differential equation 2. Errors associated with discretization of the partial differential equation 3. Uncertainties in the parameters of the engineering model 4. Errors associated with floating point operations on a digital computer
While the appropriateness of a partial differential equation to a given physical problem is beyond the scope of this chapter, the remaining three sources of errors and uncertainties can be bounded using the concept of interval representation and interval numbers. Quantifying the uncertainties in the results of an engineering calculation is essential to provide a reliable computing environment.
