Numerical verification of solutions for variational inequalities
type: Item
instance of: scholarly article
title: Numerical verification of solutions for variational inequalities
zbMATH Open document ID: 0919.65043
author: C. S. Ryoo
author: Mitsuhiro T. Nakao
published in: Numerische Mathematik
publication date: 1998-01-01T00:00:00Z
review text: The paper deals with the study of a numerical technique that enables to verify the existence of solutions for variational inequalities. This technique is based on the infinite-dimensional fixed point theorems and explicit error estimates for finite element approximations. Main result: A new method which automatically proves the existence of weak solutions for variational inequalities by numerical computation (the basis of given method consists of computing procedures to verify the existence and inclusion set of a solution by using Schauder's fixed point theorem), is described. Due to the finite element approximations and explicit a priori error estimates for obstacle problems, the authors present an effective verification procedure that through numerical computation generates a set, which includes the exact solution. Finally, a numerical example for an obstacle problem is presented.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49M15
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1247607
zbMATH Keywords: numerical verification
zbMATH Keywords: Schauder's fixed point theorem
zbMATH Keywords: variational inequalities
zbMATH Keywords: explicit error estimates
zbMATH Keywords: finite element
zbMATH Keywords: weak solutions
zbMATH Keywords: obstacle problems
zbMATH Keywords: numerical example
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
full work available at URL: s002110050394
OpenAlex ID: W2062697801
DOI: 10.1007/S002110050394
Recommended article: Numerical verification of solutions for variational inequalities of the second kind
Recommended article: Q3375620
Recommended article: An approach to the numerical verification of solutions for variational inequalities using Schauder fixed point theory
Recommended article: Numerical verifications of solutions for nonlinear elliptic equations
Recommended article: Numerical verification for solutions to partial differential equations
Recommended article: Q4868550
Recommended article: Numerical inclusion methods of solutions for variational inequalities
Recommended article: NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Recommended article: Numerical Verification of Solutions for Nonlinear Parabolic Problems
Recommended article: Q5051233
description: scientific article; zbMATH DE number 1247607