DeepAI AI Chat
Log In Sign Up

A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem

08/17/2021
by   T. Chaumont-Frelet, et al.
0

We introduce two a posteriori error estimators for Nédélec finite element discretizations of the curl-curl problem. These estimators pertain to a new Prager-Synge identity and an associated equilibration procedure. They are reliable and efficient, and the error estimates are polynomial-degree-robust. In addition, when the domain is convex, the reliability constants are fully computable. The proposed error estimators are also cheap and easy to implement, as they are computed by solving divergence-constrained minimization problems over edge patches. Numerical examples highlight our key findings, and show that both estimators are suited to drive adaptive refinement algorithms. Besides, these examples seem to indicate that guaranteed upper bounds can be achieved even in non-convex domains.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/04/2021

On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation

We propose a novel a posteriori error estimator for conforming finite el...
12/18/2019

A posteriori error estimates in W^1,p×L^p spaces for the Stokes system with Dirac measures

We design and analyze a posteriori error estimators for the Stokes syste...
06/16/2021

Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling

We develop the a posteriori error analysis of three mixed finite element...
05/29/2020

Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron

We prove that the minimizer in the Nédélec polynomial space of some degr...
04/22/2022

Explicit and efficient error estimation for convex minimization problems

We combine a systematic approach for deriving general a posteriori error...
08/01/2019

Goal-oriented error estimation and adaptivity in MsFEM computations

We introduce a goal-oriented strategy for multiscale computations perfor...