Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom that can be eliminated locally (cell-wise), thereby significantly reducing the size of the global problem. Although the linear system becomes more complex to analyze after static condensation of these element degrees-of-freedom, the pressure Schur complement of the original and reduced problem are the same. Using this fact, we prove spectral equivalence of this Schur complement to two simple matrices, which is then used to formulate optimal preconditioners for the statically condensed problem. Numerical simulations in two and three spatial dimensions demonstrate the good performance of the proposed preconditioners

An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field, pointwise satisfaction of the continuity equation and \emph{a priori} error estimates for the velocity that are independent of the pressure. The embedded--hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees-of-freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers. The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show computational efficiency gains over a full hybridized formulation

An embedded-hybridized discontinuous Galerkin method for the coupled Stokes-Darcy system

We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the whole domain. In the proposed scheme, coupling between the Stokes and Darcy domains is achieved naturally through the EDG-HDG facet variables. \emph{A priori} error analysis shows optimal convergence rates, and that the velocity error does not depend on the pressure. The error analysis is verified through numerical examples on unstructured grids for different orders of polynomial approximation

Surface stress of Ni adlayers on W(110): the critical role of the surface atomic structure

Puzzling trends in surface stress were reported experimentally for Ni/W(110) as a function of Ni coverage. In order to explain this behavior, we have performed a density-functional-theory study of the surface stress and atomic structure of the pseudomorphic and of several different possible 1x7 configurations for this system. For the 1x7 phase, we predict a different, more regular atomic structure than previously proposed based on surface x-ray diffraction. At the same time, we reproduce the unexpected experimental change of surface stress between the pseudomorphic and 1x7 configuration along the crystallographic surface direction which does not undergo density changes. We show that the observed behavior in the surface stress is dominated by the effect of a change in Ni adsorption/coordination sites on the W(110) surface.Comment: 14 pages, 3 figures Published in J. Phys.: Condens. Matter 24 (2012) 13500

Boom and bust: Is Stavanger becoming the New Detroit? - A comparative empirical analysis of a cornerstone economy

Master's thesis in Economic analysisThe purpose of this thesis is to examine whether Stavanger Region are showing indications of being on the same path as Detroit. An Error Correction Model is estimated on two datasets concerning Stavanger Region and Detroit. Each dataset consists of employment as the dependent variable and other macroeconomic variables. The model distinguishes between short - term and long - term dynamics. The sample period is 1999 - 2013 and 2003 - 2014 regarding Stavanger Region and Detroit respectively. The oil and gas industry in Stavanger Region and the automobile industry in Detroit are both vital in terms of regional economic growth

The covid-19 infodemic and online platforms as intermediary fiduciaries under international law

Reflecting on the covid-19 infodemic, this paper identifies different dimensions of information disorder associated with the pandemic, examines how online platform governance has been evolving in response, and reflects on what the crisis reveals about the relationship between online platforms, international law, and the prospect of regulation. The paper argues that online platforms are intermediary fiduciaries of the international public good, and for this reason regulation should be informed by relevant standards that apply to fiduciary relationships