This paper considers the finite element approximation and algebraic solution of the pure Neumann problem. Our goal is to present a concise variational framework for the finite element solution of the Neumann problem that focuses on the interplay between the algebraic and variational problems. While many of the results that stem from our analysis are known by some experts, they are seldom derive...

The computation oj quasistalionary nonhnear two-dimensional magnetic jield leadslo thejollowingproblem There is given a bounded domain Q and an open nonempty set R <= Q We are looking jor the magnetic vectorpotentialu(xu x2, t) which satisjies 1) a certain nonhnear parabolic équation and_an initial condition in R , 2) a nonhnear elhptic équation in S ~ O. — R which is the stationary case of the...

In this thesis, a high-order finite element scheme, based upon the Discontinuous Galerkin (DG) method, is introduced to solve oneand two-dimensional Elastohydrodynamic Lubrication (EHL) problems (line contact and point contact). This thesis provides an introduction to elastohydrodynamic lubrication, including some history, and a description of the underlying mathematical model which is based up...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

A boundary element formulation for the solution of multiple moving boundary problems is presented and tested herein. A heat transfer problem involving heating of solid, melting of solid and vaporisation of liquid is considered. Numerical results show that the boundary element method is more suitable and more accurate than both finite difference and finite element methods for this kind of problems

This report describes the implementation of a coupled mechanical/heat ransfer simulation using a Finite Element Interface (FEI). The FE1 is an abstraction layer, which lies between the application code and its linear solver libraries, controlling the set-up and solution of the linear system arising in the finite element simulation. The performance and scalability of the ISIS++ FE1 is examined o...

A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori...

In this paper, we introduce a simple method for the Cauchy problem. This new finite element method is based on least squares methodology with discontinuous approximations which can be implemented and analyzed easily. This discontinuous Galerkin finite element method is flexible to work with general unstructured meshes. Error estimates of the finite element solution are derived. The numerical ex...