Simple Curl-Curl-Conforming Finite Elements in Two Dimensions

DOI10.1137/20M1333390zbMath1458.65148arXiv2004.12507OpenAlexW3112228952WikidataQ114074204 ScholiaQ114074204MaRDI QIDQ5147975

Qian Zhang, Kaibo Hu, Zhimin Zhang

Publication date: 29 January 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.12507

zbMATH Keywords

finite elementsexterior calculusde Rham complexesquad-curl problems\(H(\mathrm{curl}^2)\)-conforming

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) A priori estimates in context of PDEs (35B45) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) de Rham theory in global analysis (58A12)

Related Items (16)

A priori and a posteriori error estimates for the quad-curl eigenvalue problem ⋮ Gradient recovery based finite element methods for the two-dimensional quad-curl problem ⋮ Bounded Poincaré operators for twisted and BGG complexes ⋮ A New Family of Nonconforming Elements with $H$(curl)-Continuity for the 3D Quad-Curl Problem ⋮ Superconvergence analysis of curlcurl-conforming elements on rectangular meshes ⋮ Weak Galerkin finite element methods for quad-curl problems ⋮ Nonconforming finite element Stokes complexes in three dimensions ⋮ A Family of Finite Element Stokes Complexes in Three Dimensions ⋮ An \textit{hp}-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem ⋮ Nonconforming Finite Elements for the −curl∆curl and Brinkman Problems on Cubical Meshes ⋮ \(H(\mathrm{curl}^2)\)-conforming spectral element method for quad-curl problems ⋮ The curl–curl conforming virtual element method for the quad-curl problem ⋮ Error analysis of a decoupled finite element method for quad-curl problems ⋮ Polynomial preserving recovery and a posteriori error estimates for the two-dimensional quad-curl problem ⋮ Three families of grad div-conforming finite elements ⋮ H(curl2)-conforming quadrilateral spectral element method for quad-curl problems

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