Polynomial-degree-robust \(\boldsymbol H(\mathbf{curl})\)-stability of discrete minimization in a tetrahedron

DOI10.5802/crmath.133zbMath1456.65156arXiv2005.14528OpenAlexW3118427563MaRDI QIDQ2219996

Martin Vohralík, Alexandre Ern, T. Chaumont-Frelet

Publication date: 21 January 2021

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.14528

zbMATH Keywords

curl-curl problemdiscrete minimization problemNédélec polynomial space

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) PDEs in connection with optics and electromagnetic theory (35Q60) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (5)

A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem ⋮ \(p\) -Robust Equilibrated Flux Reconstruction in \(\boldsymbol{H}(\textrm{curl})\) Based on Local Minimizations: Application to a Posteriori Analysis of the Curl-Curl Problem ⋮ Equivalence of local-best and global-best approximations in \(\boldsymbol{H}(\mathrm{curl})\) ⋮ A Polynomial-Degree-Robust A Posteriori Error Estimator for Nédélec Discretizations of Magnetostatic Problems ⋮ Stable broken 𝐻(𝑐𝑢𝑟𝑙) polynomial extensions and 𝑝-robust a posteriori error estimates by broken patchwise equilibration for the curl–curl problem

Cites Work

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• Unnamed Item

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