Stability and continuation of solutions to obstacle problems
type: Item
instance of: scholarly article
title: Stability and continuation of solutions to obstacle problems
zbMATH Open document ID: 0731.73100
DOI: 10.1016/0377-0427(91)90195-P
published in: Journal of Computational and Applied Mathematics
publication date: 1991-01-01T00:00:00Z
review text: The paper is concerned with obstacle problems in elasticity, formulated in terms of variational inequalities. Main topics are criteria for stable solutions (strict local minima of a related energy functional), and the problem of numerical continuation of solutions either with respect to a norm or with respect to an eigenvalue parameter. Theoretical results recently obtained by the authors are summarized and applied to obstacle problems for beams and plates [e.g.: J. Comput. Appl. Math. 26, No.1/2, 23-34 (1989; Zbl 0672.65040); Math. Methods Appl. Sci. 11, No.1, 95-104 (1989; Zbl 0669.65053); 9, 240-250 (1987; Zbl 0627.73052); 8, 516-532 (1986; Zbl 0613.73046)]. In particular, a survey of numerical methods is given which have been used to compute stability bounds.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74K20
zbMATH DE Number: 4209763
zbMATH Keywords: eigenvalue parameter
zbMATH Keywords: strict local minimum
zbMATH Keywords: energy functional
zbMATH Keywords: closed convex subset of real Hilbert space
zbMATH Keywords: nonlinearity of space of admissible vectors
zbMATH Keywords: optimal regularity properties of solutions
zbMATH Keywords: unilateral problem
zbMATH Keywords: bifurcation
zbMATH Keywords: obstacle problems in elasticity
zbMATH Keywords: variational inequalities
zbMATH Keywords: stable solutions
zbMATH Keywords: numerical continuation of solutions
zbMATH Keywords: stability bounds
author: Erich Miersemann
author: Hans D. Mittelmann
reviewed by: Waldemar Velte
MaRDI profile type: Publication
cites work: Variations‐ und Eigenwertprobleme zu nichtlinearen Differentialgleichungssystemen höherer Ordnung
cites work: Positive solutions of some eigenvalue problems in the theory of variational inequalities
cites work: Q4190894
cites work: Approximation of Obstacle Problems by Continuation Methods
cites work: Nonlinear eigenvalue problems in elliptic variational inequalities:a local study
cites work: Q5536163
cites work: Path following near bifurcation
cites work: Zum Differenzierbarkeitsproblem bei Variationsungleichungen höherer Ordnung
cites work: Q5730347
cites work: Q4746741
cites work: A multi-grid continuation strategy for parameter-dependent variational inequalities
cites work: Q3994823
cites work: Q5550951
cites work: �ber den geraden Knickstab mit begrenzter Durchbiegung
cites work: Q5601627
cites work: Variational inequalities
cites work: The non-linear beam via optimal control with bounded state variables
cites work: Über nichtlineare Eigenwertaufgaben in konvexen Mengen
cites work: Eigenwertaufgaben für Variationsungleichungen
cites work: Eigenvalue problems for variational inequalities
cites work: Zur Lösungsverzweigung bei Variationsungleichungen mit einer Anwendung auf den Knickstab mit begrenzter Durchbiegung
cites work: Stabilitätsprobleme für Eigenwertaufgaben bei Beschränkungen für die Variationen mit einer Anwendung auf die Platte
cites work: A free boundary problem and stability for the nonlinear beam
cites work: A free boundary problem and stability for the circular plate
cites work: On the continuation for variational inequalities depending on an eigenvalue parameter
cites work: Continuation for parametrized nonlinear variational inequalities
cites work: A free boundary problem and stability for the rectangular plate
cites work: On the Stability in Obstacle Problems with Applications to the Beam and Plate
cites work: Extension of Beckert's Continuation Method to Variational Inequalities
cites work: Stability in Obstacle Problems for the von Karman Plate
cites work: On the approximate solution of nonlinear variational inequalities
cites work: Bifurcation problems for discrete variational inequalities
cites work: An Efficient Algorithm for Bifurcation Problems of Variational Inequalities
cites work: A Pseudo-Arclength Continuation Method for Nonlinear Eigenvalue Problems
cites work: On Continuation for Variational Inequalities
cites work: Q5186812
cites work: Positive solutions of variational inequalities: A degree-theoretic approach
description: scientific article; zbMATH DE number 4209763