Rigorous a priori error bounds for oating-point computations are derived. We will show that using interval tools in combination with function and operator overloading such bounds can be computed on a computer automatically in a very convenient way. The bounds are of worst case type. They hold uniformly for the speci ed domain of input values. That means, whenever the oating point computation is...

1. Lax Equivalence Theorem 1 2. Abstract error analysis 2 3. Application: Finite Difference Method 3 4. Application: Finite Element Method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming Finite Element Methods 8 8. Application: Finite Volume Method 8 9. Application: Superconvergence of linear finite e...

The knowledge we have of the physical world is obtained by doing experiments and making measurements. It is important to understand how to express such data and how to analyze and draw meaningful conclusions from it. In doing this it is crucial to understand that all measurements of physical quantities are subject to uncertainties. It is never possible to measure anything exactly. “Error” in ex...