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In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data…

Numerical Analysis · Mathematics 2024-09-23 Erik Burman , Cuiyu He , Mats G. Larson

For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…

Numerical Analysis · Mathematics 2024-10-18 Dietmar Gallistl , Shudan Tian

In this paper, we design the first residual type a posteriori error estimator for mixed interior penalty discontinuous Galerkin method for the H(curl)-elliptic problems. Then we prove that our residual based a posteriori error indicator is…

Numerical Analysis · Mathematics 2023-01-05 Ming Tang , Xiaoqing Xing , Liuqiang Zhong

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Numerical Analysis · Mathematics 2024-06-12 Sören Bartels , Alex Kaltenbach

We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat…

Numerical Analysis · Mathematics 2011-04-06 Alan Demlow , Omar Lakkis , Charalambos Makridakis

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 derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…

Numerical Analysis · Mathematics 2025-06-27 Marcus J. Grote , Omar Lakkis , Carina Santos

This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…

Numerical Analysis · Computer Science 2017-05-25 Bärbel Holm , Svetlana Matculevich

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

Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…

Numerical Analysis · Mathematics 2015-02-02 Vishwas Rao , Adrian Sandu

We present a simple method for \emph{a posteriori} removal of a significant fraction of the density-fitting error from the calculated total coupled-cluster energies. The method treats the difference between the exact and density-fitted…

Chemical Physics · Physics 2020-02-20 Michał Lesiuk

We derive a computable a posteriori error estimator for the $\alpha$-harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator…

Numerical Analysis · Mathematics 2015-05-20 Long Chen , Ricardo H. Nochetto , Enrique Otárola , Abner J. Salgado

We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a…

Numerical Analysis · Mathematics 2020-10-13 Yuwen Li , Ludmil Zikatanov

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 this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint…

Optimization and Control · Mathematics 2021-08-09 Kamana Porwal , Pratibha Shakya

We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…

Numerical Analysis · Mathematics 2021-07-16 Difeng Cai , Zhiqiang Cai

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

Numerical Analysis · Mathematics 2018-06-15 Arbaz Khan , Catherine E. Powell , David J. Silvester

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

In this paper we develop a new a posteriori error analysis for the Monge-Amp\`ere equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization…

Numerical Analysis · Mathematics 2019-12-06 Jamal Adetola , Koffi Wilfrid Houedanou , Bernardin Ahounou

A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…

Numerical Analysis · Mathematics 2022-02-21 Alex Bespalov , David J. Silvester