In this paper, we are concerned with the error analysis for the finite element solution of the two-dimensional exterior Neumann boundary value problem in acoustics. In particular, we establish an explicit priori error estimates in H and Lnorms including both the effect of the truncation of the DtN mapping and that of the numerical discretization. To apply the finite element method (FEM) to the ...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

In this paper, the Neumann boundary value problem for Beltrami operator is explicitly solved in a circular ring domain, solvability conditions are also given explicit forms. Moreover, second-order operators with Bitsadze/Laplace as main part combinations of Cauchy-Riemann and investigated.

As a model of the second order elliptic equation with non-trivial boundary conditions, we consider the Laplace equation with mixed Dirichlet and Neumann boundary conditions on convex polygonal domains. Our goal is to establish that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon-Miranda) discrete maximum principle, and then p...

Suppose M is a compact manifold with boundary ∂M . Let M̃ be a normal covering of M . Suppose (A, T ) is an elliptic differential boundary value problem on M with lift (Ã, T̃ ) to M̃ . Then the von Neumann dimension of kernel and cokernel of this lift are defined. The main result of this paper is: These numbers are finite, and their difference, by definition the von Neumann index of (Ã, T̃ ), equal...

A non-overlapping domain decomposition algorithm of Neumann–Neumann type for solving variational inequalities arising from the elliptic boundary value problems in two dimensions with unilateral boundary condition is presented. We suppose that boundary with inequality condition is ‘relatively’ small. First, the linear auxiliary problem, where the inequality condition is replaced by the equality ...