The Faculty of Mathematics and Natural Sciences: Mathematisch-Naturwissenschaftliche Fakultät: Recent submissions
Now showing items 581-600 of 5046
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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 ... -
Understanding the evolution of Boraginales: insights from morphology, phylogeny, biogeography and taxonomy
(2024-08-14)Boraginales are a medium-sized angiosperm order within Lamiids, with very diverse fruit morphology, which has been traditionally used for nomenclatural subdivisions. This thesis attempts to elucidate some aspects of the ... -
Totalsynthesis of Pentamycin
(2024-08-14)The polyene macrolide pentamycin, first isolated from Streptomyces penticus in 1958, displays impressive biological activities against various pathogens, including Trichomonas vaginalis or Candida albicans, and can be used ... -
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>)), ... -
ε-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs
(2017)In this article, we present a cost-benefit analysis of the approximation in tensor products of Hilbert spaces of Sobolev-analytic type. The Sobolev part is defined on a finite dimensional domain, whereas the analytical ... -
Low-rank approximation to heterogeneous elliptic problems
(2017-03)In this work, we investigate the low-rank approximation of elliptic problems in heterogeneous media by means of Kolmogrov <em>n</em>-width and asymptotic expansion. This class of problems arises in practical applications ... -
Second order optimality conditions for optimal control of quasilinear parabolic equations
(2017-03)We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality ... -
On the expected uniform error of geometric Brownian motion approximated by the Lévy-Ciesielski construction
(2017-06)It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show ... -
Singular value decomposition versus sparse grids: Refined complexity estimates
(2017)We compare the cost complexities of two approximation schemes for functions which live on the product domain <em>Ω<sub>1</sub></em> × <em>Ω<sub>2</sub></em> of sufficiently smooth domains <em>Ω<sub>1</sub></em> ⊂ ... -
On the convergence rate of sparse grid least squares regression
(2017-08)While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, ... -
A collection of nonsmooth Riemannian optimization problems
(2017-09)Nonsmooth Riemannian optimization is a still scarcely explored subfield of optimization theory that concerns the general problem of minimizing (or maximizing), over a domain endowed with a manifold structure, a real-valued ... -
A representer theorem for deep kernel learning
(2019-05)In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical ... -
Tangent and normal cones for low-rank matrices
(2017-10)In [D. R. Luke, <em>J. Math. Imaging Vision</em>, 47(3):231-238, 2013] the structure of the Mordukhovich normal cone to varieties of low rank matrices at rank-deficient points has been determined. A simplified proof of ... -
Upscaled HDG methods for Brinkman equations with high-contrast heterogeneous coefficient
(2017-10)In this paper, we present new upscaled HDG methods for Brinkman equations in the context of high-contrast heterogeneous media. The a priori error estimates are derived in terms of both fine and coarse scale parameters that ... -
Stochastic subspace correction in Hilbert space
(2017-11)We consider an incremental approximation method for solving variational problems in infinite-dimensional separable Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite ...
