[Dottorcomp] Seminari di Matematica Applicata, 17/02/2026, Theophile Chaumont-Frelet

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 17 Febbraio 2026, alle *ore 15* precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Theophile Chaumont-Frelet (INRIA, Lille)

terrà un seminario dal titolo:

A posteriori error estimation and adaptivity for the finite element
discretization of second-order PDE problems set in unbounded domains.

Abstract: This talk is dedicated to the discretization of second-order PDE
problems set in unbounded domains. The approximation procedure for such
problems is typically divided into two steps. First (i), a modeling error
is introduced by truncating the domain at a finite distance 𝐿 from the
origin. Then (ii), the remaining bounded domain is meshed and the
corresponding finite element space is used in the discretization. Standard
a posteriori error estimators for this problem only take into account the
error incurred in step (ii), but disregard the modeling error introduced in
step (i).

I will discuss an alternative viewpoint where the whole domain is
discretized by an infinite mesh, on which a finite-dimensional finite
element space of degree is constructed. The construction of the finite
element space implicitly involves a truncation procedure, so that the
situation is formally identical to the standard setting. However, the key
insight of this interpretation is that one can construct an error estimator
that accounts for all the sources of error induced by the discretization.
This estimator can in particular steer adaptive mesh refinement algorithms
that automatically adjust the truncation of the domain.

I will rigorously show that the proposed estimator is reliable and
efficient, and that the corresponding adaptive algorithm converges at
optimal rates. I will also present numerical examples illustrating these
theoretical findings.

Part of these results are based on a joint work with Gregor Gantner.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/