Hamburger Beiträge zur Angewandten Mathematik POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks

Hamburger Beiträge zur Angewandten Mathematik

We consider a simplified accoustic model to describe nonlinear phenomena occuring in loudspeakers. The simplification is that we restrict to the one–dimensional isentropic Euler equations in a slab, where on the right end a membrane is moving periodically with frequency ω and maximal displacement ε œ 1. The asymptotic model based on the small parameter ε yields hyperbolic first order systems, w...

Hamburger Beiträge zur Angewandten Mathematik A Nonlinear Model Predictive Concept for Control of Two-Phase Flows Governed by the Cahn-Hilliard Navier-Stokes System

We present a nonlinear model predictive framework for closedloop control of two-phase flows governed by the Cahn-Hilliard NavierStokes system. We adapt the concept for instantaneous control from [6, 12, 16] to construct distributed closed-loop control strategies for twophase flows. It is well known that distributed instantaneous control is able to stabilize the Burger’s equation [16] and also t...

Hamburger Beiträge zur Angewandten Mathematik A Simplified Model for Non-Isothermal Crystallization of Polymers

Recently, Burger and Capasso [M3AS 11 (2001) 1029–1053] derived a coupled system of partial differential equations to describe non–isothermal crystallization of polymers. The system is based on a spatial averaging of the underlying stochastic birth–and–growth process describing the nucleation and growth of single crystals. In the present work we reconsider the scaling properties of the dimensio...

Hamburger Beiträge zur Angewandten Mathematik A Priori Error Estimates for a Finite Element Discretization of Parabolic Optimization Problems with Pointwise Constraints in Time on Mean Values of the Gradient of the State

This article is concerned with the discretization of parabolic optimization problems subject to pointwise in time constraints on mean values of the derivative of the state variable. Central component of the analysis are a priori error estimates for the dG(0)-cG(1) discretization of the parabolic partial differential equation (PDE) in the L∞(0, T ;H1 0 (Ω))-norm, together with corresponding esti...

Hamburger Beiträge zur Angewandten Mathematik Continuous Convergence of Relations - A Principle in Discretization Procedures