A Posteriori Error Estimation for Hierarchic Models of Elliptic Boundary Value Problems on Thin Domains

DOI10.1137/0733013zbMath0846.65056OpenAlexW2084862534MaRDI QIDQ4875499

Publication date: 26 September 1996

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0733013

zbMATH Keywords

error estimation heat conduction elliptic boundary value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (23)

Estimates of the modeling error generated by homogenization of an elliptic boundary value problem ⋮ A Posteriori Modeling Error Estimates for the Assumption of Perfect Incompressibility in the Navier--Stokes Equation ⋮ A new Korn's type inequality for thin domains and its application to iterative methods ⋮ Adaptive \(hpq\)-finite element methods of hierarchical models for plate- and shell-like structures ⋮ Convergence and stability analyses of hierarchic models of dissipative second order evolution equations ⋮ A priori modeling error estimates of hierarchical models for elasticity problems for plate- and shell-like structures ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ THE PARTIAL HOMOGENIZATION: CONTINUOUS AND SEMI-DISCRETIZED VERSIONS ⋮ Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations ⋮ 3D-based hierarchical models and \(hpq\)-approximations for adaptive finite element method of Laplace problems as exemplified by linear dielectricity ⋮ Application of an automatic \(hp\) adaptive finite element method for thin-walled structures ⋮ Adaptive \(hpq\) finite element methods for the analysis of 3D-based models of complex structures. Part II: A posteriori error estimation ⋮ Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. I: Hierarchical modeling and approximations ⋮ The \(hp\) finite element method for problems in mechanics with boundary layers ⋮ Dimensional reduction for the beam in elasticity on a bounded domain ⋮ Error estimates and adaptive finite element methods ⋮ Estimates of dimension reduction errors for stationary reaction-diffusion problems ⋮ Numerical Analysis of the Adiabatic Variable Method for the Approximation of the Nuclear Hamiltonian ⋮ Boundary layer resolution in hierarchical models of laminated composites ⋮ Hierarchical models of thin elastic structures: overview and recent advances in error estimation and adaptivity ⋮ Local error estimation for dimensional reduction: application to special geometries ⋮ Dimensional reduction for the plate in elasticity on an unbounded domain. ⋮ Local error estimation for dimensionally reduced models of elliptic boundary value problems.

This page was built for publication: A Posteriori Error Estimation for Hierarchic Models of Elliptic Boundary Value Problems on Thin Domains