A \(p\)-version finite element method for nonlinear elliptic variational inequalities in 2D

DOI10.1007/s00211-006-0035-0zbMath1133.65042OpenAlexW1981178078MaRDI QIDQ861656

Andreas Krebs, Ernst Peter Stephan

Publication date: 30 January 2007

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-006-0035-0

zbMATH Keywords

convergencefinite element methodnumerical experiments\(p\)-versionobstacle problemmesh refinementa priori error estimatenonlinear elliptic variational inequalitiessecond-order quasi-linear elliptic operators

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Newton-type methods (49M15)

Related Items (15)

Hybridization and stabilization for \textit{hp}-finite element methods ⋮ On the \(p\)-version approximation in the boundary element method for a variational inequality of the second kind modelling unilateral contact and given friction ⋮ \(hp\)-adaptive IPDG/TDG-FEM for parabolic obstacle problems ⋮ Coupling regularization and adaptive \(hp\)-BEM for the solution of a delamination problem ⋮ Comparison of mixed \(hp\)-BEM (stabilized and non-stabilized) for frictional contact problems ⋮ Goal-oriented error control in adaptive mixed FEM for Signorini's problem ⋮ A posteriori error estimates of \(hp\)-adaptive IPDG-FEM for elliptic obstacle problems ⋮ Full discretisations for nonlinear evolutionary inequalities based on stiffly accurate Runge-Kutta and \(hp\)-finite element methods ⋮ Quasi-optimal degree distribution for a quadratic programming problem arising from the \(p\)-version finite element method for a one-dimensional obstacle problem ⋮ Stabilized mixed \(hp\)-BEM for frictional contact problems in linear elasticity ⋮ Biorthogonal basis functions in \(hp\)-adaptive FEM for elliptic obstacle problems ⋮ Mixed finite element methods for two-body contact problems ⋮ Higher order FEM for the obstacle problem of the \(p\)-Laplacian -- a variational inequality approach ⋮ Higher order mixed FEM for the obstacle problem of the \(p\)-Laplace equation using biorthogonal systems ⋮ A Strongly Convergent Combined Relaxation Method in Hilbert Spaces

Uses Software

• LANCELOT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A generalized conjugate gradient algorithm for solving a class of quadratic programming problems
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. II: The Trace Spaces and Application to the Boundary Value Problems with Nonhomogeneous Boundary Conditions
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
• Error Estimates for the Approximation of a Class of Variational Inequalities
• A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables

This page was built for publication: A \(p\)-version finite element method for nonlinear elliptic variational inequalities in 2D