A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem
type: Item
instance of: scholarly article
title: A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem
zbMATH Open document ID: 1166.78006
author: B. E. Eshmatov
published in: Numerische Mathematik
publication date: 2008-08-20T00:00:00Z
review text: The authors study a nonconforming finite element method with weakly continuous \(P_1\) vector fields for a two-dimensional curl-curl and grad-div problem. To control the consistency error two term involving the jumps of the vector field across element boundaries are included in the discrete equations. Nearly optimal convergence rates are established on graded meshes, which are confirmed by numerical experiments.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 5314411
zbMATH Keywords: curl-curl and grad-div problem
zbMATH Keywords: nonconforming finite element methods
zbMATH Keywords: Maxwell equations
MaRDI profile type: Publication
full work available at URL: s00211-008-0149-7
OpenAlex ID: W2085830137
cites work: Q4239076
cites work: Q4865314
cites work: Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: The singular complement method.
cites work: Time-dependent Maxwell's equations with charges in singular geometries
cites work: Q4426214
cites work: Resolution of the Maxwell equations in a domain with reentrant corners
cites work: Q3126801
cites work: Improving the rate of convergence of `high order finite elements' on polygons and domains with cusps
cites work: A mixed displacement-based finite element formulation for acoustic fluid-structure interaction
cites work: Finite element computation of the vibration modes of a fluid-solid system
cites work: L2-Theory of the Maxwell operator in arbitrary domains
cites work: A Singular Field Method for the Solution of Maxwell's Equations in Polyhedral Domains
cites work: Q3369398
cites work: A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
cites work: A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations
cites work: Q4531674
cites work: Augmented formulations for solving Maxwell equations
cites work: Q4162607
cites work: A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
cites work: A coercive bilinear form for Maxwell's equations
cites work: Maxwell and Lamé eigenvalues on polyhedra
cites work: Singularities of electromagnetic fields in polyhedral domains
cites work: Weighted regularization of Maxwell equations in polyhedral domains. A rehabilitation of Nodal finite elements
cites work: EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS
cites work: Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
cites work: Finite Element Methods for Navier-Stokes Equations
cites work: Q3470840
cites work: Q4023365
cites work: A displacement method for the analysis of vibrations of coupled fluid‐structure systems
cites work: A Singular Field Method for Maxwell's Equations: Numerical Aspects for 2D Magnetostatics
cites work: Finite elements in computational electromagnetism
cites work: Q5526485
cites work: Finite Element Methods for Maxwell's Equations
cites work: Elliptic problems in domains with piecewise smooth boundaries
cites work: Mixed finite elements in \(\mathbb{R}^3\)
cites work: A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
cites work: Error estimates for the finite element approximation to a maxwell-type boundary value problem
cites work: An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
cites work: A local compactness theorem for Maxwell's equations
cites work: A remark on a compactness result in electromagnetic theory
DOI: 10.1007/S00211-008-0149-7
description: scientific article; zbMATH DE number 5314411