A cell conservative flux recovery technique is developed here for vertexcentered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant free a posteriori error estimator which is proven to be reliable and efficient. Some numerical tests ...

The finite volume method combines the advantage of the finite element method and the finite difference method, while overcoming their shortcomings. This paper describes the development of the finite volume method and the process of using finite volume method for fluid calculations. Finally, this paper introduces the process of using improved finite volume method for solving the flow equations o...

Volume free electron laser uses volume distributed feedback (VDFB), which can essentially reduce the threshold current of generation and provides the possibility of smooth frequency tuning. An undulator VFEL is considered.

In this paper we count the number of cusps of minimal non-compact finite volume arithmetic hyperbolic 3-orbifolds. We show that for each N , the orbifolds of this kind which have exactly N cusps lie in a finite set of commensurability classes, but either an empty or an infinite number of isometry classes.

Article history: Received 28 March 2008 Available online 13 November 2008 Submitted by J. Guermond

In this paper we will show that on any complete noncompact Riemannian manifold with a finite volume there exist uncountably many geodesic loops of arbitrarily small length.

In this paper, we classify all the hyperbolic non-compact Coxeter polytopes of finite volume combinatorial type of which is either a pyramid over a product of two simplices or a product of two simplices of dimension greater than one. Combined with results of Kaplinskaja [5] and Esselmann [3] this completes the classification of hyperbolic Coxeter n-polytopes of finite volume with n + 2 facets.

In this article, we consider complete, n-dimensional, Riemannian manifolds of finite volume. We assume that the Ricci curvature is bounded from below and normalized to have the lower bound given by Ric M ≥ −(n − 1).

For a compact Riemannian manifold, Weyl’s law describes the asymptotic behavior of the counting function of the eigenvalues of the associated Laplace operator. In this paper we discuss Weyl’s law in the context of automorphic forms. The underlying manifolds are locally symmetric spaces of finite volume. In the non-compact case Weyl’s law is closely related to the problem of existence of cusp fo...