We show that if L is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of L are all in the interval (−δ, δ) for a fixed δ ∈ [0, 1) and no complimentary region of L is an interval bundle over a surface, then each boundary leaf of L has a nontrivial fundamental group. We also prove existence of a fixed constant δ0 > 0 such that i...

In this paper, we prove that every closed nil 3-manifold is diffeomorphic to a cusp cross-section of a finite volume complex hyperbolic 2-orbifold.

Article history: Received 25 May 2012 Received in revised form 14 September 2012 Accepted 21 November 2012 Available online 19 December 2012

We introduce a simple new Eulerian method for treatment of moving boundaries in compressible fluid computations. Our approach is based on the extension of the interface tracking method recently introduced in the context of multifluids. The fluid domain is placed in a rectangular computational domain of a fixed size, which is divided into Cartesian cells. At every discrete time level, there are ...

In this paper we describe a one-dimensional adaptive moving mesh method and its application to hyperbolic conservation laws from magnetohydrodynamics (MHD). The method is robust, because it employs automatic control of mesh adaptation when a new model is considered, without manually-set parameters. Adaptive meshes are a common tool for increasing the accuracy and reducing computational costs wh...

We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.

We review the spatial discretization procedure for three high-order, unstructured grid methods recently developed for use within ocean circulation modeling. They are based respectively on spectral finite element and high-order finite volume formulations. We discuss and contrast the three methods in the context of the shallow water equations.

A new volume deformation technique using FEM and voxel-texture (voxture) maps has been developed. In contrast to the traditional deformation techniques, the new algorithm is aimed at volume transformations, deformations and volume metamorphosis.

A space-time Finite Volume method is devised to simulate incompressible viscous flows in an evolving domain. Inspired by the ADER (based on a Finite-Element-prediction/Finite-Volume-correction approach), Navier-Stokes equations are discretized onto overset grid which able take into account both shape of possibly moving object and evolution compact transmission condition employed order mutually ...

Abstract. A semidiscrete finite volume element (FVE) approximation to a parabolic integrodifferential equation (PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimalorder L2-error estimate for smooth initial data and nearly the same optimal-order L2-error estimate for nonsmooth initial data are obtained. More precisely, for homogeneous equations, an elementary energy techni...