Some aspects of numerical realization of the optimal finite-element method for a biharmonic problem with boundary conditions of the second type
type: Item
instance of: scholarly article
title: Some aspects of numerical realization of the optimal finite-element method for a biharmonic problem with boundary conditions of the second type
zbMATH Open document ID: 0948.65128
DOI: 10.1007/BF02667926
author: O. M. Lytvyn
author: K. V. Nosov
published in: Cybernetics and Systems Analysis
publication date: 2000-04-03T00:00:00Z
review text: The variational problem under approximation is connected with the equation \(\Delta^2 u=f\) and rectangular grids. The first iteration of the method is a standard finite element approximation with bipolynomial spline spaces (Hermitian cubic polynomials are used). The authors discuss the possibility to decrease the obtained approximation of the minimal value of the energy functional via passing the new basic functions. For them the authors suggest a system of ordinary differential equations and give analytical expressions. For the new spaces it is necessary to solve a new system on the grid. Convergence of the iterations is not proved but the authors consider the method as ``comparable'' with traditional ones (they and the grids in experiments are not specified).
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1418925
zbMATH Keywords: finite-element method
zbMATH Keywords: biharmonic problem
zbMATH Keywords: convergence
zbMATH Keywords: spline spaces
reviewed by: Evgeniĭ Dyakonov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02667926
OpenAlex ID: W2068919809
description: scientific article; zbMATH DE number 1418925