What is ... a-posteriori error estimation?

Vortrag von Nis-Erik Bohne

Datum: 18.11.25  Zeit: 16.30 - 18.30  Raum:

Error analysis is a integral part of numerical mathematics. The classical way of doing this- called apriori error analysis- only provides an asymptotic result that involves the exact solution, which is generally unknown, and requires some regularity assumptions on the exact solution. Therefore the a-priori analysis only provides a qualitative result. A-posteriori error analysis on the other hand does not require any regularity assumptions nor any knowledge of the exact solution and provides a computable upper bound to the error.

In this talk we will be considering the Poisson model problem in 2d and use the finite element method to approximate the exact solution. We then will develop an a-posteriori error estimator from first principles and prove that this estimator truly is an upper bound to the error. We will then use the error estimator to motivate an adaptive mesh refinement strategy for approximating solutions with point singularities in order to recover optimal convergence rates. The talk closes by a short discussion on an open problem in the field of adaptive finite element methods.