The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 561-580 of 5046
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A new generalization of the P1 non-conforming FEM to higher polynomial degrees
(2015)This paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation ... -
A multiscale finite element method for Neumann problems in porous microstructures
(2015-01)In this paper we develop and analyze a Multiscale Finite Element Method (MsFEM) for problems in porous microstructures. By solving local problems throughout the domain we are able to construct a multiscale basis that can ... -
Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering
(2015-03)We present and analyze a pollution-free Petrov-Galerkin multiscale finite element method for the Helmholtz problem with large wave number <em>κ</em> as a variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard ... -
Hyperbolic cross approximation in infinite dimensions
(2015)We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analytic-type smoothness in the infinite-dimensional ... -
Numerical verification of a bond-based softening peridynamic model for small displacements: Deducing material parameters from classical linear theory
(2016-12)In this article we present a systematic numerical approach for calibration and numerical verification of peridynamics models. The approach is illustrated for a two parameter exponential bond softening model, which is ... -
Extraction of fragments and waves after impact damage in particle-based simulations
(2016-12)The analysis of simulation results and the verification against experimental data is essential to develop and interpret simulation models for impact damage. We present two visualization techniques to post-process particle-based ... -
Simulation of wave propagation and impact damage in brittle materials using peridynamics
(2016-12)In this paper we present the results of simulating wave propagation and impact damage in brittle materials, like ceramics, using peridynamics, a non-local generalization of continuum mechanics. Two different bond-based ... -
Line search algorithms for locally Lipschitz functions on Riemannian manifolds
(2016-11)This paper presents line search algorithms for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we generalize the so-called Wolfe conditions for nonsmooth functions on Riemannian ... -
Additive Schwarz solvers for hp-FEM discretizations of PDE-constrained optimzation problems
(2016-10)In this paper, we investigate the minimization of a quadratic functional subject to a boundary value problem of a second order linear elliptic partial differential equation. There are no inequality constraints for state ... -
A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization
(2016-10)In this paper, a nonsmooth optimization method for locally Lipschitz functions on real algebraic varieties is developed. To this end, the set-valued map <em>ε</em>-conditional subdifferential <em>x</em> → ... -
Robust numerical upscaling of elliptic multiscale problems at high contrast
(2016-01)We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of <em>H<sup>1</sup></em> into the image ... -
Relaxing the CFL condition for the wave equation on adaptive meshes
(2017-02)The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size ... -
An adaptive multiscale approach for electronic structure methods
(2016)In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr¨odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the bond ... -
Numerical simulation of the temporal evolution of a three dimensional barchanoid dune and the corresponding sediment dynamics
(2016-09)In this paper we present the results of the numerical simulation of a three-dimensional current-driven sediment transport process. In detail, the temporal evolution of a barchanoid dune is studied. Two phenomena are treated ... -
Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with disorder potentials
(2016-08)This paper analyses the numerical solution of a class of non-linear Schrödinger equations by Galerkin finite elements in space and a mass- and energy conserving variant of the Crank-Nicolson method due to Sanz-Serna in ... -
Computation of local and quasi-local effective diffusion tensors in elliptic homogenization
(2016-08)This paper gives a re-interpretation of the multiscale method of Målqvist and Peterseim [Math. Comp. 2014] by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the ... -
Adaptive mesh refinement strategies in isogeometric analysis: A computational comparison
(2016-05)We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two ... -
Sampling inequalities for sparse grids
(2015)Sampling inequalities play an important role in deriving error estimates for various reconstruction processes. They provide quantitative estimates on a Sobolev norm of a function, defined on a bounded domain, in terms of ... -
A-posteriori error estimation of discrete POD models for PDE-constrained optimal control
(2016-03)In this work a-posteriori error estimates for linear-quadratic optimal control problems governed by parabolic equations are considered. Different error estimation techniques for finite element discretizations and model-order ... -
A priori L2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints
(2016-03)In this paper, an elliptic optimization problem with pointwise inequality constraints on the state is considered. The main contribution of this paper are a priori <em>L<sup>2</sup></em>-error estimates for the discretization ...
