The boundary concentrated finite element method is a variant of the hp-version of the finite element method that is particularly suited for the numerical treatment of elliptic boundary value problems with smooth coefficients and low regularity boundary conditions. For this method we present two multilevel preconditioners that lead to preconditioned stiffness matrices with condition numbers that...

We study the uniform approximation of boundary layer functions exp(−x/d) for x ∈ (0, 1), d ∈ (0, 1], by the p and hp versions of the finite element method. For the p version (with fixed mesh), we prove super-exponential convergence in the range p+ 1/2 > e/(2d). We also establish, for this version, an overall convergence rate of O(p−1 √ lnp) in the energy norm error which is uniform in d, and sh...

and this problem can be solved analytically: u (x) = x − sinhx/sinh1. The purpose of starting with this problem is to demonstrate the fundamental concepts and pitfalls in FEM in a situation where we know the correct answer, so that we will know where our approximation is good and where it is poor. In cases of practical interest we will look at ODEs and PDEs that are too complex to be solved ana...

Finite element methods are based on the variational formulation of partial differential equations which only need to compute the gradient of a function. Although unknowns are still associated to nodes, the function composed by piece-wise polynomials on each element and thus the gradient can be computed element-wise. Finite element spaces can thus be constructed on general triangulations and thi...

Abstract — In this paper, we present a non-conforming hp computational modeling methodology for solving elasticity problems. We consider the incompressible elasticity model formulated as a mixed displacement-pressure problem on a global domain which is partitioned into several local subdomains. The approximation within each local subdomain is designed using div-stable hp-mixed finite elements. ...

The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems describes the elasticity of the structure in Lagrangian form and describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form. Interactions between Lagrangian and Eulerian...

This paper considers some refined versions of the Inverse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers of PQ.

Superconvergence phenomenon of the Legendre spectral collocation method and the p-version finite element method is discussed under the one dimensional setting. For a class of functions that satisfy a regularity condition (M): ‖u‖L∞ ≤ cMk on a bounded domain, it is demonstrated, both theoretically and numerically, that the optimal convergent rate is supergeometric. Furthermore, at proper Gaussia...

An analysis of developing and fully developed turbulent flow was carried out when different techniques have been used in a zone close to the solid wall. In this paper, wall element technique based on the finite element method (FEM) has been adopted and compared with other techniques for determination of confined turbulent flow with a one equation model used to depict the turbulent viscosity is ...