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We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…

Numerical Analysis · Mathematics 2023-02-01 Philip L. Lederer , Rolf Stenberg

A residual based {\em a posteriori} error estimator is derived for a quadratic finite element method (fem) for the elliptic obstacle problem. The error estimator involves various residuals consisting the data of the problem, discrete…

Numerical Analysis · Mathematics 2014-04-14 Thirupathi Gudi , Kamana Porwal

In two dimensions, we propose and analyze an a posteriori error estimator for finite element approximations of the stationary Navier Stokes equations with singular sources on Lipschitz, but not necessarily convex, polygonal domains. Under a…

Numerical Analysis · Mathematics 2019-10-14 Alejandro Allendes , Enrique Otarola , Abner J. Salgado

A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…

Numerical Analysis · Mathematics 2026-04-28 Muhammad Afzal , Naveed Ahmed , Volker John

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

In this paper, we study the "a posteriori" error estimate corresponding to the Brinkman-Darcy-Forchheimer problem. We introduce the variational formulation discretised by using the finite element method. Then, we establish an "a posteriori"…

Numerical Analysis · Mathematics 2021-04-29 Toni Sayah

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

We propose a cheaper version of \textit{a posteriori} error estimator from arXiv:1707.00057 for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator…

Numerical Analysis · Mathematics 2017-10-25 Olga Gorynina , Alexei Lozinski , Marco Picasso

We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…

Optimization and Control · Mathematics 2025-05-08 Francisco Fuica , Nicolai Jork

We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…

Numerical Analysis · Mathematics 2024-02-28 T. Chaumont-Frelet

We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…

Numerical Analysis · Mathematics 2021-05-05 T. Chaumont-Frelet , A. Ern , M. Vohralík

In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new…

Numerical Analysis · Mathematics 2020-04-10 Koffi Wilfrid Houédanou , Jamal Adetola

We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…

Numerical Analysis · Mathematics 2015-07-30 Fernando D. Gaspoz , Pedro Morin , Andreas Veeser

Residual-based a~posteriori error estimators are derived for the modified Morley FEM, proposed by Wang, Xu, Hu [J. Comput. Math, 24(2), 2006], for the singularly perturbed biharmonic equation and the nonlinear von K\'arm\'an equations. The…

Numerical Analysis · Mathematics 2026-02-17 A. K. Dond , D. Gallistl , S. Nayak , M. Schedensack

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

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 present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…

Numerical Analysis · Mathematics 2012-05-15 Kristoffer Selim , Anders Logg , Mats G. Larson

We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error…

Numerical Analysis · Mathematics 2021-08-04 T. Chaumont-Frelet , S. Lanteri , P. Vega

We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…

Numerical Analysis · Mathematics 2026-02-26 Franco Dassi , Rekha Khot , Andres E. Rubiano , Ricardo Ruiz-Baier

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