Séminaire ACSIOM :

Le 21 janvier 2025 à 13:15 - salle 109 (1er étage)

Présentée par Bulle Raphaël - INRIA Nancy, équipe MIMESIS

Adaptive multi-mesh FEM for the spectral fractional Laplacian

Fractional partial differential equations have gained interest in the last 10 years due to their ability to model anomalous diffusion and non-local behavior with a relatively small number of parameters. These advantages come with drawbacks from the numerical perspective as these problems raise new challenges when we try to solve them with computers. In this talk we are interested in a particular fractional problem, based on the spectral fractional Laplacian operator. More specifically, we look at the discretization and the design of adaptive mesh refinement strategies to efficiently solve such problem numerically. To do so we consider a particular framework based on a rational scheme coupled with a finite element method. We derive an a posteriori error estimator for the finite element discretization error which is then used to steer an adaptive refinement loop. Finally, we will introduce you to a novel multi-mesh adaptive refinement algorithm taking advantage of the rational scheme to further optimize the discretization.