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Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

Numerical Analysis · Mathematics 2022-11-28 Yangshuai Wang , Hao Wang

In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery…

Numerical Analysis · Mathematics 2016-07-13 Zhiqiang Cai , Shuhao Cao , Rob Falgout

In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…

Numerical Analysis · Mathematics 2025-07-09 Thomas Führer , Sergio Rojas

An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is…

Numerical Analysis · Mathematics 2017-04-26 Andrea Cangiani , Emmanuil H. Georgoulis , Tristan Pryer , Oliver J. Sutton

In this paper we analyze a posteriori error estimates for a mixed formulation of the linear elasticity eigenvalue problem. A posteriori estimators for the nearly and perfectly compressible elasticity spectral problems are proposed. With a…

Numerical Analysis · Mathematics 2022-01-12 Felipe Lepe , Gonzalo Rivera , Jesús Vellojín

We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…

Numerical Analysis · Mathematics 2016-09-16 Shaohong Du , Runchang Lin , Zhimin Zhang

In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…

Numerical Analysis · Mathematics 2016-11-24 Annalisa Buffa , Eduardo M. Garau

We derive a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound is obtained by a splitting of the equation into a linear stochastic partial…

Numerical Analysis · Mathematics 2022-01-24 Ľubomír Baňas , Christian Vieth

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Duran, C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix-Raviart non-conforming finite elements. In…

Numerical Analysis · Mathematics 2014-11-11 Daniele Boffi , Ricardo G. Durán , Francesca Gardini , Lucia Gastaldi

This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…

Numerical Analysis · Mathematics 2016-11-23 E. H. van Brummelen , S. Zhuk , G. J. van Zwieten

We present functional-type a posteriori error estimates in isogeometric analysis. These estimates, derived on functional grounds, provide guaranteed and sharp upper bounds of the exact error in the energy norm. {Moreover, since these…

Numerical Analysis · Mathematics 2014-09-23 Stefan K. Kleiss , Satyendra K. Tomar

The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error…

Numerical Analysis · Mathematics 2020-04-20 Yinnian He , Weizhang Huang

Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by…

Numerical Analysis · Mathematics 2025-12-24 Philipp Weder , Annalisa Buffa

This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…

Numerical Analysis · Mathematics 2026-01-30 Jingshi Li , Jiachuan Zhang

This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…

Numerical Analysis · Mathematics 2021-12-17 Taiga Nakano , Xuefeng Liu

We introduce two a posteriori error estimators for N\'ed\'elec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager-Synge identity and an associated equilibration procedure. They are reliable and…

Numerical Analysis · Mathematics 2021-08-24 T. Chaumont-Frelet

This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…

Numerical Analysis · Mathematics 2021-10-06 Ludovic Chamoin , Frederic Legoll

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…

Numerical Analysis · Mathematics 2026-02-04 Lutz Angermann

A posteriori error estimator is derived for an elliptic interface problem in the fictitious domain formulation with distributed Lagrange multiplier considering a discontinuous Lagrange multiplier finite element space. A posteriori error…

Numerical Analysis · Mathematics 2024-07-02 Najwa Alshehri , Daniele Boffi , Lucia Gastaldi

We propose a posteriori error estimators for classical low-order inf-sup stable and stabilized finite element approximations of the Stokes problem with singular sources in two and three dimensional Lipschitz, but not necessarily convex,…

Numerical Analysis · Mathematics 2019-01-30 Alejandro Allendes , Enrique Otarola , Abner J. Salgado