English
Related papers

Related papers: Robust a posteriori error control for the Allen-Ca…

200 papers

The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a…

Numerical Analysis · Mathematics 2017-09-06 Fleurianne Bertrand , Marcel Moldenhauer , Gerhard Starke

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

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

We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed…

Numerical Analysis · Mathematics 2021-09-27 Daniele Antonio Di Pietro , Ilaria Fontana , Kyrylo Kazymyrenko

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

Numerical Analysis · Mathematics 2022-11-28 Yangshuai Wang , Hao Wang

We propose a new residual-based a posteriori error estimator for discontinuous Galerkin discretizations of time-harmonic Maxwell's equations in first-order form. We establish that the estimator is reliable and efficient, and the dependency…

Numerical Analysis · Mathematics 2025-02-03 T. Chaumont-Frelet , P. Vega

We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the…

Numerical Analysis · Mathematics 2015-04-24 Michael Feischl , Gregor Gantner , Dirk Praetorius

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

Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…

Numerical Analysis · Mathematics 2025-03-26 Ying Liu , Jingjing Xiao , Nianyu Yi , Huihui Cao

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

The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…

Numerical Analysis · Mathematics 2016-08-30 Alejandro Allendes , Enrique Otarola , Richard Rankin , Abner J. Salgado

We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…

Numerical Analysis · Mathematics 2024-06-12 Jan Giesselmann , Kiwoong Kwon

The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…

Numerical Analysis · Mathematics 2016-11-25 Andreas Buhr , Christian Engwer , Mario Ohlberger , Stephan Rave

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

In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general…

Numerical Analysis · Mathematics 2024-01-15 Abhinav Jha

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time…

Numerical Analysis · Mathematics 2023-05-03 Yaoyao Chen , Yunqing Huang , Nianyu Yi , Peimeng Yin

In this paper, we present a posteriori error estimation for weak Galerkin method applied to fourth order singularly perturbed problem. The weak Galerkin discretization space and numerical scheme are first described. A fully computable…

Numerical Analysis · Mathematics 2025-10-02 Shicheng Liu , Qilong Zhai

We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to…

Numerical Analysis · Mathematics 2026-01-22 T. Chaumont-Frelet

We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013,…

Numerical Analysis · Mathematics 2014-06-18 Erik Burman

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper,…

Machine Learning · Statistics 2021-03-08 Masahiro Fujisawa , Takeshi Teshima , Issei Sato , Masashi Sugiyama