Notes on Finite Element Modeling
Abstract: It is important to make a clear distinction between numerical simulation and finite element modeling: 1. In numerical simulation an idea of a physical reality is precisely stated in the form of mathematical equations. Model form errors, uncertainties in input data, and the errors of numerical approximation are estimated and controlled separately. This is possible only if the underlying mathematical problem (such as a problem of continuum mechanics) is well posed and the numerical problem satisfies the requirements of consistency and stability. 2. In finite element modeling, on the other hand, a numerical problem is constructed by piecing together elements from the element library of a finite element analysis (FEA) software product without providing evidence that the underlying mathematical problem is well posed and the numerical problem satisfies the requirements of consistency and stability. Therefore, we cannot assume that numerical convergence will exist, or that a numerical error can be computed.