For the numerical treatment of Hammerstein equations by variational methods which has been considered by Hertling, we establish the stability in the sense of Mikhlin, Stetter and Tucker. Introduction. If one uses a variational method for the numerical treatment of Hammerstein equations, one obtains a nonlinear algebraic system of equations. In order to investigate the stability of the computing...

In this paper we analyze the error as well for semi-discretization full discretization of a time-dependent convection-diffusion problem. We use in space local discontinuous Galerkin (LDG) method on class layer-adapted meshes including Shishkin-type and Bakhvalov-type implicit θ-scheme time. For piecewise tensor-product polynomials degree k obtain uniform or almost estimates with respect to orde...

Existence, uniqueness and error estimates for Ritz-Galerkin methods are o discussed in the case where the associated bilinear form satisfies a Carding type inequality, i.e., it is indefinite in a certain way. An application to the finite element method is given. In this note, we would like to discuss existence, uniqueness and estimates over the whole domain for some Ritz-Galerkin methods where ...

The following estimate for the Rayleigh–Ritz method is proved: |λ̃−λ||(ũ,u)| ≤ ‖Aũ− λ̃ũ‖sin∠{u;Ũ}, ‖u‖= 1. Here A is a bounded self-adjoint operator in a real Hilbert/euclidian space, {λ,u} one of its eigenpairs, Ũ a trial subspace for the Rayleigh–Ritz method, and {λ̃, ũ} a Ritz pair. This inequality makes it possible to analyze the fine structure of the error of the Rayleigh–Ritz method, in part...

In the paper, forced transverse vibration of fractional viscoelastic Euler-Bernoulli is studied. Based on relationship stress and strain, partial differential equation describing beam considered. The Riemann-Liouville derivative order used. Using Ritz-Galerkin method, transformed into a system equations containing derivatives. dynamic response simply supported to harmonic concentrated force cal...

The Web-method is a meshless finite element technique which uses weighted extended B-splines (Web-splines) on a tensor product grid as basis functions. It combines the computational advantages of B-splines and standard mesh-based elements. In particular, degree and smoothness can be chosen arbitrarily without substantially increasing the dimension. Hence, accurate approximations are obtained wi...

The purpose of this paper is to first show how an Euler-Lagrange theorem can be applied to the steady-state fluvial landscape model, thereby allowing the geomorphic solution surfaces to be understood as those that globally optimize the difference between kinetic and potential energy dissipation (Hamilton’s Principle) while conserving mass. It is then shown how this variational formulation of th...