INS Preprints: INS Preprints: Neuzugänge
Anzeige der Dokumente 81-100 von 153
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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 ... -
A priori error estimates for state constrained semilinear parabolic optimal control problems
(2016-02)We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In contrast to many results in numerical analysis ... -
Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d
(2016-06)We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard ... -
Localized Coulomb descriptors for the Gaussian Approximation Potential
(2016-02)We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system ... -
Nonconforming P1 elements on distorted triangulations: Lower bounds for the discrete energy norm error
(2016)Compared to conforming P1 finite elements, nonconforming P1 finite element discretizations are thought to be less sensitive to the appearance of distorted triangulations. E.g., optimal-order discrete <em>H<sup>1</sup></em> ... -
Stable splittings of Hilbert spaces of functions of infinitely many variables
(2016)We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction ... -
Numerical stochastic homogenization by quasi-local effective diffusion tensors
(2017-02)This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal ... -
On the decay rate of the singular values of bivariate functions
(2017-11)In this work, we establish a new truncation error estimate of the singular value decomposition (SVD) for a class of Sobolev smooth bivariate functions <em>κ</em> ∈ <em>L<sup>2</sup></em>(Ω, <em>H<sup>s</sup></em>(<em>D</em>)), ...
