Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems

DOI10.1007/s00211-019-01075-1zbMath1447.65130OpenAlexW2979360014WikidataQ126862899 ScholiaQ126862899MaRDI QIDQ2288367

Difeng Cai, Shun Zhang, Zhi-qiang Cai

Publication date: 17 January 2020

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

Full work available at URL: https://doi.org/10.1007/s00211-019-01075-1

zbMATH Keywords

finite element methoda posteriori error estimatorsecond-order boundary value problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Physics-informed distribution transformers via molecular dynamics and deep neural networks ⋮ Robust flux reconstruction and a posteriori error analysis for an elliptic problem with discontinuous coefficients ⋮ Primal-Dual Reduced Basis Methods for Convex Minimization Variational Problems: Robust True Solution a Posteriori Error Certification and Adaptive Greedy Algorithms ⋮ Generalized Prager-Synge identity and robust equilibrated error estimators for discontinuous elements ⋮ Uniform high-order convergence of multiscale finite element computation on a graded recursion for singular perturbation

Cites Work

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• Equilibrated residual error estimates are \(p\)-robust
• Adaptive finite element methods for elliptic equations with non-smooth coefficients
• A hybrid a posteriori error estimator for conforming finite element approximations
• The polynomial-preserving recovery for higher order finite element methods in 2D and 3D
• Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements
• Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
• Equilibrated error estimators for discontinuous Galerkin methods
• Superconvergent Derivative Recovery for Lagrange Triangular Elements of Degreepon Unstructured Grids
• Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements
• A Note on Constant-Free A Posteriori Error Estimates
• Error Estimate Procedure in the Finite Element Method and Applications
• A simple error estimator and adaptive procedure for practical engineerng analysis
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• On the poisson equation with intersecting interfaces
• A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
• Convergence of Adaptive Finite Element Methods
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Mixed Finite Element Methods and Applications
• Stable broken $H^1$ and $H(\mathrm {div})$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions
• A Posteriori Error Estimators for the Raviart–Thomas Element
• Equilibrated residual error estimator for edge elements
• Approximations in elasticity based on the concept of function space
• Finite Elements
• A posteriori error estimators for elliptic equations with discontinuous coefficients

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