Moving Dirichlet boundary conditions

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...

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed f...

Absorption semigroups and dirichlet boundary conditions

Dirichlet-to-neumann Boundary Conditions for Multiple Scattering Problems

A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact nonreflecting boundary condition for the situation, where the computational domain and its ex...

Wentzell boundary conditions in the context of Dirichlet forms

Let X be a locally compact space, m a Radon measure on X, h a regular Dirichlet form in L2(X,m). For a Radon measure μ we interpret h as a regular Dirichlet form τ in L2(m+μ). We show that μ decomposes as μr +μs where μr is coupled to h and μs decouples from h. Additionally to this ‘space perturbation’, a second perturbation is introduced by a measure ν describing absorption. The main object of...