Let X be a symmetric space of non-compact type and Γ\X a locally symmetric space. Then the bottom spectrum λ1(Γ\X) satisfies the inequality λ1(Γ\X) ≤ λ1(X). We show that if equality λ1(Γ\X) = λ1(X) holds, then Γ\X has either one end, which is necessarily of infinite volume, or two ends, one of infinite volume and another of finite volume. In the latter case, Γ\X is isometric to R1 ×N endowed wi...

We study error estimates for a finite volume discretization of an elliptic equation. We prove that, for s ∈ [0,1], if the exact solution belongs to H1+s and the right-hand side is f + div(G) with f ∈ L2 and G ∈ (Hs)N , then the solution of the finite volume scheme converges in discrete H1norm to the exact solution, with a rate of convergence of order hs (where h is the size of the mesh).

a r t i c l e i n f o a b s t r a c t Numerical schemes for ideal magnetohydrodynamics (MHD) that are based on the standard finite volume method (FVM) exhibit pseudo-convergence in which irregular structures no longer exist only after heavy grid refinement. We describe a method for obtaining solutions for coplanar and near-coplanar cases that consist of only regular structures, independent of g...

We calculate the magnetic dipole moment of the ∆ baryon using a background magnetic field on 2+1-flavors of clover fermions on anisotropic lattices. We focus on the finite volume effects that can be significant in background field studies, and thus we use two different spatial volumes in addition to several quark masses.

Following the previous work of Qiu and Shu [SIAM J. Sci. Comput., 31 (2008), 584-607], we investigate the performance of Hermite weighted essentially non-oscillatory (HWENO) scheme for nonconvex conservation laws. Similar to many other high order methods, we show that the finite volume HWENO scheme performs poorly for some nonconvex conservation laws. We modify the scheme around the nonconvex r...

Let X be a Hadamard manifold and Γ ⊂ Isom(X) a discrete group of isometries which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the limit set of Γ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessarily compact or finite volume manifolds.

Let X be a symmetric space of non-compact type and Γ\X a locally symmetric space. Then the bottom spectrum λ1(Γ\X) satisfies the inequality λ1(Γ\X) ≤ λ1(X). We show that if equality λ1(Γ\X) = λ1(X) holds, then Γ\X has either one end, which is necessarily of infinite volume, or two ends, one of infinite volume and another of finite volume. In the latter case, Γ\X is isometric to R1 ×N endowed wi...

Article history: Received 21 May 2013 Received in revised form 12 November 2013 Accepted 18 January 2014 Available online 23 January 2014

This paper describes a numerical solution for two dimensional partial differential equations modeling (or arising from) a fluid flow and transport phenomena. The diffusion equation is discretized by the Nodal methods. The saturation equation is solved by a finite volume method. We start with incompressible single-phase flow and move step-by-step to the black-oil model and compressible two phase...

We prove the Hijazi inequality, an estimate for Dirac eigenvalues, for complete manifolds of finite volume. Under some additional assumptions on the dimension and the scalar curvature, this inequality is also valid for elements of the essential spectrum. This allows to prove the conformal version of the Hijazi inequality on conformally parabolic manifolds if the spin analog to the Yamabe invari...