**Seminar Numerische Mathematik**

WIAS Berlin

#### Prof. L. Heltai (SISSA, Italien)

## Immersed Finite Element Methods for interface and fluid structure interaction problems: An overview and some recent results

**Programm / Abstract:**

Immersed Finite Element Methods (IFEM) are an evolution of the original Immersed Boundary Element Method (IBM) developed by Peskin in the early seventies for the simulation of complex Fluid Structure Interaction (FSI) problems. In the IBM, the coupled FSI problem is discretised using a single (uniformly discretised) background fluid solver, where the presence of the solid is taken into account by adding appropriate forcing terms in the fluid equation. Approximated Dirac delta distributions are used to interpolate between the Lagrangian and the Eulerian framework in the original formulation by Peskin, while a variational formulation was introduced by Boffi and Gastaldi (2003), and later generalised by Heltai and Costanzo (2012). By carefully exploiting the variational definition of the Dirac distribution, it is possible to reformulate the discrete Finite Element problem using non-matching discretisations without recurring to Dirac delta approximation.

One of the key issues that kept people from adopting IBM or IFEM techniques is related to the loss in accuracy attributed to the non-matching nature of the discretisation between the fluid and the solid domains, leading to solvers that converge only sub-optimally.

In this talk I will present a brief overview of Immersed Finite Element Methods, and will present some recent results that exploit techniques introduced by D?Angelo and Quarteroni (2012), to show that, for the variational finite element formulation, the loss in accuracy is only restricted to a thin layer of elements around the solid-fluid interface, and that optimal error estimates in all norms are recovered if one uses appropriate weighted norms when measuring the error.

**Zeit:**

am Dienstag den 28. März 2017 um 14:30

**Ort:**

Weierstraß-Institut

Mohrenstr. 39

10117 Berlin

Erhard-Schmidt-Hörsaal Erdgeschoss

*eingetragen von lawrenz(marion.lawrenz@wias-berlin.de, 030 20372566)*

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