Seminari del Dipartimento di Matematica

Seminario del 2024

Michele Ruggeri

A gentle introduction to adaptive finite element methods for partial differential equations

nell'ambito della serie: TOPICS IN MATHEMATICS 2023/2024

In any context of life, human beings aim to achieve the best possible result with minimal effort. In this talk, we discuss how to implement this general principle to the numerical approximation of partial differential equations, where the aim is to obtain accurate approximations at low computational costs. Using the approximation of the Poisson equation by standard finite element methods as a prototypical example, we show how adaptive algorithms based on rigorous a posteriori error estimation lead to approximations that are, in a certain sense, optimal.