Matthias Langer

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In this paper, we develop a new stability and convergence theory for highly indefinite elliptic partial differential equations by considering the Helmholtz equation at high wave number as our model problem. The key element in this theory is a novel k-explicit regularity theory for Helmholtz boundary value problems that is based on decomposing the solution(More)
Higher order finite element methods are applied to 2D and 3D second order elliptic interface problems with smooth interfaces, and their convergence is analyzed in the H1and L2-norm. The error estimates are expressed explicitly in terms of the approximation order p and a parameter δ that quantifies the mismatch between the smooth interface and the finite(More)
We present an a priori analysis of the hp-version of the finite element method for the primal formulation of frictional contact in linear elasticity. We introduce a new limiting case estimate for the interpolation error at Gauss and Gauss-Lobatto quadrature points. An hp-adaptive strategy is presented; numerical results shows that this strategy can lead to(More)
Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their(More)
This paper describes an absolute localisation method for an unmanned ground vehicle (UGV) if GPS is unavailable for the vehicle. The basic idea is to combine an unmanned aerial vehicle (UAV) to the ground vehicle and use it as an external sensor platform to achieve an absolute localisation of the robotic team. Beside the discussion of the rather naive(More)
Diffusive moment equations with an arbitrary number of moments are formally derived from the semiconductor Boltzmann equation employing a moment method and a Chapman-Enskog expansion. The moment equations are closed by employing a generalized Fermi-Dirac distribution function obtained from entropy maximization. The current densities allow for a(More)