TECHNISCHE UNIVERSITÄT BERLIN Finite Element Decomposition and Minimal Extension for Flow Equations

TECHNISCHE UNIVERSITÄT BERLIN Moving Dirichlet Boundary Conditions

This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet bound...

TECHNISCHE UNIVERSITÄT BERLIN Regularization of Constrained PDEs of Semi-Explicit Structure

A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented. The given procedure works for semi-explicit operator DAEs of first order which includes the Navier-Stokes and other flow equations. This reformulation is a regularization in the sense that a semi-discretization in space leads to a DAE of lower index, i.e., of differentiation index 1 instead ...

Technische Universität Berlin Institut für Mathematik Fundamental Diagrams and Multiple Pedestrian Streams

Technische Universität Berlin Institut für Mathematik Some Fundamental Considerations for the Application of Macroscopic Models in the Field of Pedestrian Crowd Simulation

Optimal Thickness of a Cylindrical Shell – an Optimal Control Problem in Linear Elasticity Theory∗

In this paper we discuss optimization problems for cylindrical tubes which are loaded by an applied force. This is a problem of optimal control in linear elasticity theory (shape optimization). We are looking for an optimal thickness minimizing the deflection (deformation) of the tube under the influence of an external force. From basic equations of mechanics, we derive the equation of deformat...