For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, n...

where x = (x1, . . . , xd) ∈ IR , t > 0. HJ equations arise in many practical areas such as differential games, mathematical finance, image enhancement and front propagation. It is well known that solutions of (1) are Lipschitz continuous but derivatives can become discontinuous even if the initial data is smooth. There is a close relation between HJ equations and hyperbolic conservation laws. ...

Currently used finite volume methods are essentially low order methods. In this paper, we present a systematic way to derive higher order finite volume schemes from higher order mixed finite element methods. Mostly for convenience but sometimes from necessity, our procedure starts from the hybridization of the mixed method. It then approximates the inner product of vector functions by an approp...

" A rheological model has been derived for the linear-viscoelastic behaviour of a dispersion of transversely rigid spherical capsules. The model incorporates finite thickness of the elastic shell o f the capsules, anisotropy of the mechanical propert ies o f the interface and finite volume fraction. The dynamic viscosity of the dispersion is calculated. The influence of the microstructural para...

in this paper, the temperature distribution around a moving heat source had been investigated including the phase change and non phase change . in non-phase change state, the governing equation was converted to finite difference equation by finite volume method and the equation was solved by alternating direction implicit method. this method was unconditionally stable . in phase change state, t...

1. In [12] and [13] Selberg introduced a trace formula for a compact, locally symmetric space of negative curvature. There is a natural algebra of operators on any such space which commute with the Laplacian. The Selberg trace formula gives the trace of these operators. Selberg also pointed out the importance of deriving such a formula when the symmetric space is assumed only to have finite vol...

We consider properly immersed finite topology minimal surfaces Σ in complete finite volume hyperbolic 3-manifolds N , and in M × S, where M is a complete hyperbolic surface of finite area. We prove Σ has finite total curvature equal to 2π times the Euler characteristic χ(Σ) of Σ, and we describe the geometry of the ends of Σ. .