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Related papers: Robust a-posteriori error estimates for weak Galer…

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We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This method combines a nonlinear penalty formulation with a discontinuous Galerkin-based residual…

Numerical Analysis · Mathematics 2020-11-24 Roberto J. Cier , Sergio Rojas , Victor M. Calo

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

We present a fully computable a posteriori error estimator for piecewise linear finite element approximations of reaction-diffusion problems with mixed boundary conditions and piecewise constant reaction coefficient formulated in arbitrary…

Numerical Analysis · Mathematics 2015-07-06 Mark Ainsworth , Tomáš Vejchodský

We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…

Numerical Analysis · Mathematics 2014-07-17 Zhiqiang Cai , Shun Zhang

The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-field PDE model in which the Young's modulus is an affine…

Numerical Analysis · Mathematics 2018-10-18 Arbaz Khan , Alex Bespalov , Catherine E. Powell , David J. Silvester

This article introduces a simple weak Galerkin (WG) finite element method for solving convection-diffusion-reaction equation. The proposed method offers significant flexibility by supporting discontinuous approximating functions on general…

Numerical Analysis · Mathematics 2026-01-06 Chunmei Wang , Shangyou Zhang

This paper introduces a novel a posteriori error estimation framework for the enriched Galerkin (EG) finite element method applied to linear parabolic equations. While the EG method has been recognized for its local conservation property…

Numerical Analysis · Mathematics 2026-04-29 Hyun-Geun Shin , Yi-Yung Yang , Sanghyun Lee

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Numerical Analysis · Mathematics 2017-04-24 Alejandro Allendes , Enrique Otarola , Richard Rankin

For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…

Numerical Analysis · Mathematics 2016-03-04 Zhiqiang Cai , Cuiyu He , Shun Zhang

We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in…

Numerical Analysis · Mathematics 2022-01-13 Assyr Abdulle , Giacomo Rosilho de Souza

In this article, a reliable and efficient a posteriori error estimator of residual type is derived for a class of discontinuous Galerkin methods for the frictional contact problem with reduced normal compliance which is modeled as a…

Numerical Analysis · Mathematics 2021-04-19 Kamana Porwal , Tanvi

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…

Numerical Analysis · Computer Science 2018-05-16 Svetlana Matculevich , Monika Wolfmayr

A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…

Numerical Analysis · Mathematics 2015-03-26 Shaohong Du , Xiaoping Xie

A posteriori error estimators are studied for discontinuous Galerkin methods for solving a frictional contact problem, which is a representative elliptic variational inequality of the second kind. The estimators are derived by relating the…

Numerical Analysis · Mathematics 2014-01-21 Fei Wang , Weimin Han

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 devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…

Numerical Analysis · Mathematics 2015-04-13 Stephen Arthur Metcalfe

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…

Numerical Analysis · Mathematics 2021-06-17 Martin Eigel , Oliver Ernst , Björn Sprungk , Lorenzo Tamellini

In this article we present an a posteriori error estimator for the spatial-stochastic error of a Galerkin-type discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the…

Numerical Analysis · Mathematics 2019-02-22 Jan Giesselmann , Fabian Meyer , Christian Rohde

This work concerns with the discontinuous Galerkin (DG)method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary…

Numerical Analysis · Mathematics 2015-06-11 Thi Hong Cam Luong , Christian Daveau

In this study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part…

Numerical Analysis · Mathematics 2025-05-06 Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan