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We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator…

Numerical Analysis · Mathematics 2010-11-04 Emmanuel Creusé , Serge Nicaise , Emmanuel Verhille

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 provide a unified analysis of a posteriori and a priori error bounds for a broad class of discontinuous Galerkin and $C^0$-IP finite element approximations of fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs…

Numerical Analysis · Mathematics 2021-03-24 Ellya L. Kawecki , Iain Smears

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…

Numerical Analysis · Mathematics 2017-05-12 Long Chen , Jun Hu , Xuehai Huang , Hongying Man

We address the error control of Galerkin discretization (in space) of linear second order hyperbolic problems. More specifically, we derive a posteriori error bounds in the L\infty(L2)-norm for finite element methods for the linear wave…

Numerical Analysis · Mathematics 2017-05-17 Emmanuil H. Georgoulis , Omar Lakkis , Charalambos Makridakis

We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…

Numerical Analysis · Mathematics 2024-05-10 Francisco Fuica , Felipe Lepe , Pablo Venegas

The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the $C^0$ interior penalty, and the WOPSIP schemes. Those methods are modified…

Numerical Analysis · Mathematics 2022-03-08 Carsten Carstensen , Neela Nataraj

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…

Numerical Analysis · Mathematics 2016-11-24 Michael Feischl , Gregor Gantner , Alexander Haberl , Dirk Praetorius

We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving eigenvalue problems associated with second…

Numerical Analysis · Mathematics 2016-03-16 Lin Lin , Benjamin Stamm

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

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

We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…

Numerical Analysis · Mathematics 2017-08-01 Martin Licht , Matthias Maier

We present an equilibration-based a posteriori error estimator for N\'ed\'elec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for N\'ed\'elec elements of…

Numerical Analysis · Mathematics 2021-05-26 Joscha Gedicke , Sjoerd Geevers , Ilaria Perugia , Joachim Schöberl

Two residual-type error estimators for the mortar staggered discontinuous Galerkin discretizations of second order elliptic equations are developed. Both error estimators are proved to be reliable and efficient. Key to the derivation of the…

Numerical Analysis · Mathematics 2019-08-12 Lina Zhao , Eric Chung

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

An a posteriori error bound for the pointwise error of the quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of…

Numerical Analysis · Mathematics 2024-01-05 Rohit Khandelwal , Kamana Porwal , Tanvi Wadhawan

Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…

Numerical Analysis · Mathematics 2017-07-20 Natalia Kopteva

We propose a robust a posteriori error estimator for the hybridizable discontinuous Galerkin (HDG) method for convection-diffusion equations with dominant convection. The reliability and efficiency of the estimator are established for the…

Numerical Analysis · Mathematics 2014-12-18 Huangxin Chen , Jingzhi Li , Weifeng Qiu

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…

Numerical Analysis · Mathematics 2023-03-22 Jiachuan Zhang , Ran Zhang , Xiaoshen Wang