A partition of unity approach to fluid mechanics and fluid-structure interaction.

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach.

Finite element approximation of the Laplace-Beltrami operator on a surface with boundary.

We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche's method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order in the energy and norms that take the approximation of the surface and the boundary into account.

[Phobia or fear in rural communities].

In the following paper an attempt is made to demonstrate by means of phobia that neurotic subjective experience can only be understood in its social environment. Patients with phobic symptoms far more frequently come from rural communities and small towns, i.e.