Generalized Finite Element Systems for smooth differential forms and Stokes problem

We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously introduced notion of Finite Element Systems, and the examples include conforming mixed finite elements for Stokes' equation. In dimension 2 we detail four low order finite element complexes and one infinite family of highorder finite element complexes. In dimension 3 we define one low order complex, which may be branched into Whitney forms at a chosen index. Stokes pairs with continuous or discontinuous pressure are provided in arbitrary dimension. The finite element spaces all consist of composite polynomials. The framework guarantees some nice properties of the spaces, in particular the existence of commuting interpolators. It also shows that some of the examples are minimal spaces.Comment: v1: 27 pages. v2: 34 pages. Numerous details added. v3: 44 pages. 8 figures and several comments adde

On variational eigenvalue approximation of semidefinite operators

Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As an alternative, we show here how the abstract theory can be developed in terms of a geometric property called the vanishing gap condition. This condition is shown to be equivalent to eigenvalue convergence and intermediate between two different discrete variants of Friedrichs estimates. Next we turn to a more practical means of checking these properties. We introduce a notion of compatible operator and show how the previous conditions are equivalent to the existence of such operators with various convergence properties. In particular the vanishing gap condition is shown to be equivalent to the existence of compatible operators satisfying an Aubin-Nitsche estimate. Finally we give examples demonstrating that the implications not shown to be equivalences, indeed are not.Comment: 26 page

A structure preserving numerical discretization framework for the Maxwell Klein Gordon equations in 2D

International audienc

A structure preserving numerical discretization framework for the Maxwell Klein Gordon equations in 2D

International audienc

Central Bank Modernization

The broad-based technical cooperation program between the Reserve Bank of Malawi (RBM), the International Monetary Fund (IMF) and Norges Bank1, which has supported the Malawian authorities’ efforts to strengthen and modernize the RBM since 2006, has some unique features that have led us to regard it as a pilot program. We therefore considered it worthwhile to issue an Occasional Paper covering the objectives, framework and subject areas of the program. This Occasional Paper will cover the program’s implementation up to end-2009. While the articles provide guidance on the background against which choices and recommendations were advocated, the achievements of the program are not fully articulated given the ongoing nature of the technical cooperation program. We hope that the articles will provide helpful information and guidance for other central banks and institutions aiming to modernize and professionalize their policy conduct