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In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes [Jha20.CAMWA] to the newly proposed algebraic stabilization schemes…

Numerical Analysis · Mathematics 2024-04-04 Abhinav Jha

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

This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…

Numerical Analysis · Mathematics 2022-02-24 Georges Semaan , Toni Sayah , Faouzi Triki

We introduce a residual-based a posteriori error estimator for a novel $hp$-version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimensions. We prove that the error estimate provides an upper…

Numerical Analysis · Mathematics 2021-02-16 Zhaonan Dong , Lorenzo Mascotto , Oliver J. Sutton

This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…

Numerical Analysis · Mathematics 2025-11-14 Yuwen Li

This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise symmetric and H(div)-conforming stress approximation.…

Numerical Analysis · Mathematics 2017-05-25 C. Carstensen , D. Gallistl , J. Gedicke

We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…

Numerical Analysis · Mathematics 2019-04-02 Kathrin Smetana , Olivier Zahm , Anthony T Patera

In this paper, a residual-type a posteriori error estimator is proposed and analyzed for a modified weak Galerkin finite element method solving linear elasticity problems. The estimator is proven to be both reliable and efficient because it…

Numerical Analysis · Mathematics 2023-02-21 Liu Chunmei , Zhong Liuqiang , Xie Yingying Xie , Zhou Liping

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

We derive functional a posteriori error equalities and constant free two sided estimates for certain types of partial differential equations. The error is measured in a combined norm which takes into account both the primal and dual…

Analysis of PDEs · Mathematics 2015-12-29 Immanuel Anjam , Dirk Pauly

In this work, we analyze the residual-based a posteriori error estimation of the multi-scale cancer invasion model, which is a system of three non-stationary reaction-diffusion equations. We present the numerical results of a study on a…

Numerical Analysis · Mathematics 2023-11-07 Gopika P. B. , Nishant Ranwan , Nagaiah Chamakuri

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

Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary…

Numerical Analysis · Mathematics 2020-10-29 Stefan Kurz , Dirk Pauly , Dirk Praetorius , Sergey Repin , Daniel Sebastian

We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We…

Numerical Analysis · Mathematics 2010-09-17 Serge Nicaise , Juliette Venel

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding…

Numerical Analysis · Mathematics 2015-03-17 Xiaobo Yin , Hehu Xie

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 introduce novel a posteriori error indicators for a nonlinear least-squares solver for smooth solutions of the Monge--Amp\`ere equation on convex polygonal domains in $\mathbb{R}^2$. At each iteration, our iterative scheme decouples the…

Numerical Analysis · Mathematics 2025-09-09 Alexandre Caboussat , Anna Peruso , Marco Picasso

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

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

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