2. From data to information

2.1 Discretization and data

Mathematical models aim to describe an often highly complex physical reality. The model must be faithful to reality, and this fidelity requires that the predictions the model provides are consistent with observed reality. Only in this case can the model replace reality, and thus lighten design tasks in the various fields of engineering, where repeated experiments prove very costly both in terms of budget and design and implementation time.

However, these models involve highly complex equations (often involving partial derivatives), which are coupled, highly non-linear and defined in domains of complex geometry. The solution of these models yields the value of a quantity of interest u, which may be scalar, vector or tensor (e.g. temperature,...