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.

frictional shear stress is usually determined by utilizing the coefficient of friction or the constant friction factor models. the present study deals with finite element analysis of double cup extrusion process to determine the relationship between constant friction factor (m) and coefficient of friction (µ), since the metal flow in this process is very sensitive to frictional conditions. ther...

We examine condition numbers, preconditioners, and iterative methods for finite element discretizations of coercive PDEs in the context of the fundamental solvability result, the Lax-Milgram Lemma. Working in this Hilbert space context is justified because finite element operators are restrictions of infinite-dimensional Hilbert space operators to finite-dimensional subspaces. Moreover, useful ...

An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial di erential equations de ned on random domains. This method is based on a mariage between the eXtended Finite Element Method and spectral stochastic methods. In this paper, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random g...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

A two-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow is presented. The main attraction of this approach is that it exploits all the benefits of the spectral methods with the versatility of the finite element method. In addition, it is not affected by the disadvantage of the spectral methods used in volume discretization to create denser systems. To achie...

As detailed in recent reports [2 §1; 3; & op. cit. therein], a need has long been well established and many investigations undertaken at NCAR and elsewhere, to create high-resolution numerical simulation methods for atmospheric dynamics, that are accurate similarly to spectral methods and computationally efficient similarly to finite-element type methods. Two research codes that demonstrate the...

We provide a detailed presentation and discussion of a numerical modeling technique for earthquake dynamics based on the spectral element method. The problem of dynamic frictional contact along slip interfaces in elastic domains is formulated in a hybrid variational form, with Lagrange multipliers associated to the fault tractions. The problem is discretized in space by a spectral element metho...