Functional a posteriori error estimates for the parabolic obstacle problem

DOI10.1515/cmam-2021-0156zbMath1487.35455arXiv2109.14519OpenAlexW4207078396WikidataQ110867526 ScholiaQ110867526MaRDI QIDQ2134447

Darya E. Apushkinskaya, Sergey I. Repin

Publication date: 3 May 2022

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.14519

zbMATH Keywords

free boundaryparabolic obstacle problemfunctional a posteriori error estimates

Mathematics Subject Classification ID

Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85) Initial-boundary value problems for second-order parabolic equations (35K20) Free boundary problems for PDEs (35R35)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles
• Pointwise regularity of the free boundary for the parabolic obstacle problem
• Estimates for the difference between exact and approximate solutions of parabolic equations on the basis of Poincaré inequalities for traces of functions on the boundary
• Higher regularity of the free boundary in the parabolic Signorini problem
• Averaging techniques yield reliable a posteriori finite element error control for obstacle problems
• On the singular set of the parabolic obstacle problem
• An \(L^ 2\)-error estimate for an approximation of the solution of a parabolic variational inequality
• A posteriori estimates for partial differential equations
• Parabolic variational inequalities in one space dimension and smoothness of the free boundary
• An optimal stopping problem with linear reward
• On optimal stopping and free boundary problems
• Inéquations d'évolution paraboliques avec convexes dependant du temps. Applications aux inéquations quasi-variationnelles d'évolution
• The regularity of free boundaries in higher dimensions
• Estimates of deviations from exact solutions of elliptic variational inequalities
• Boundary estimates for solutions of the parabolic free boundary problem
• Free boundary problems. Regularity properties near the fixed boundary
• Thin obstacle problem: estimates of the distance to the exact solution
• \(L^{\infty}\)-error estimate for an approximation of a parabolic variational inequality
• Accuracy of mathematical models. Dimension reduction, homogenization, and simplification
• Guaranteed error bounds and local indicators for adaptive solvers using stabilised space-time IgA approximations to parabolic problems
• Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions
• An epiperimetric inequality approach to the parabolic Signorini problem
• On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients
• Problèmes unilateraux
• Models of phase transitions
• Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation
• Degenerate problems with irregular obstacles
• On a Variational Inequality Formulation of an Electrochemical Machining Moving Boundary Problem and its Approximation by the Finite Element Method
• Error Estimates for the Approximation of a Class of Variational Inequalities
• A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
• Regularity of a free boundary in parabolic potential theory
• Lipschitz property of the free boundary in the parabolic obstacle problem
• Sharp Estimates for Solutions of a Parabolic Signorini Problem
• Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem
• Galerkin Finite Element Methods for Parabolic Problems
• Variational inequalities
• Regularity of the solution of a problem with a two-sided constraint on the boundary for elliptic and parabolic equations

This page was built for publication: Functional a posteriori error estimates for the parabolic obstacle problem