A new technique for the implementation of cell-centered finite volume schemes is proposed. It is based on an equivalence between these schemes and the non-conforming Crouzeix-Raviart finite element approximation. Though the implementation somewhat increases the number of unknowns, it brings two significant advantages that make it attractive. On the one hand the resulting formulation is well-def...

Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space CH . The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in C equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of SU(2, 1) with Gaussia...

The possibility of neutral, brane-like solutions in a higher dimensional setting is discussed. In particular, we describe a supersymmetric solution in six dimensions which can be interpreted as a “three-brane” with a non-compact transverse space of finite volume. The construction can be generalized to n+4-dimensions and the result is a n+3-brane compactified on a n−1-dimensional Einstein manifo...

Let V be a noncompact complete Riemannian manifold. We find a geometric condition which assures that the essential spectrum of the Laplacian on V contains a half-line, by means of fiber bundle structures and the asymptotic behavior of mean curvatures on the ends of V , and give lower bounds of the essential spectrum. Our criteria can be applied to locally symmetric spaces of finite volume and m...

Let r be a geometrically finite group acting on the hyperbolic space HN+’ and let H, denote the Laplace-Beltrami operator on M = T\H”‘+ ‘, which we assume is not compact. If M is either of finite volume or cusp-free, we determine completely the Lp spectrum of Hr for 1 $ p -C co, tinding that it depends upon p in a nontrivial manner. We also obtain a number of pointwise and Lp decay properties o...

A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Recently a number of so-called well-balanced schemes were developed which satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. In most cases, applications t...

We consider the space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulas for the discretisation of the fractional derivative, to numerically solve the equation on a f...