Finite Element Solution of Boundary Value Problems with Nonlocal Jump Conditions
Journal Title: Mathematical Modelling and Analysis - Year 2008, Vol 13, Issue 3
Abstract
We consider stationary linear problems on non-connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.
Authors and Affiliations
M. Koleva
A New Strategy for Choosing the Chebyshev-Gegenbauer Parameters in a Reconstruction Based on Asymptotic Analysis
The Gegenbauer reconstruction method, first proposed by Gottlieb et. al. in 1992, has been considered a useful technique for re-expanding finite series polynomial approximations while simultaneously avoiding Gibbs artifa...
On Solutions of Neumann Boundary Value Problem for the LiƩnard Type Equation
We provide conditions on the functions [i]f(x) [/i]and [i]g(x)[/i], which ensure the existence of solutions to the Neumann boundary value problem for the equation [i]x''+f(x)[sup][/sup]x[sup]'2[/sup]+g(x)=0.[/i]
Characteristic Functions for Sturm-Liouville Problems with Nonlocal Boundary Conditions
This paper presents some new results on a spectrum in a complex plane for the second order stationary differential equation with one Bitsadze--Samarskii type nonlocal boundary condition. In this paper, we survey the char...
Finite Element Solution of Boundary Value Problems with Nonlocal Jump Conditions
We consider stationary linear problems on non-connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element me...
On Dependence of Sets of Functions on the Mean Value of their Elements
The paper considers, for a given closed bounded set $Msubset {mathbb R}^m$ and $K=(0,1)^nsubset {mathbb R}^n$, the set ${mathcal M}= { hin L_2(K;{mathbb R}^m)mid h(x) in M,,a.e.,xin K}$ and its subsets [ {mathcal M}(hat...