On the \(p\)- and \(hp\)-extension of Nédélec's curl-conforming elements

DOI10.1016/0377-0427(92)00127-UzbMath0820.65066MaRDI QIDQ1343652

Peter B. Monk

Publication date: 17 September 1995

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

error estimatesfinite elementsLegendre polynomialedge elementscurl-conforming elementsmagnetostatics problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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) Electro- and magnetostatics (78A30)

Related Items

Quasioptimality of some spectral mixed methods ⋮ Spectral element discretization of the Maxwell equations ⋮ An analysis of Nédélec's method for the spatial discretization of Maxwell's equations ⋮ A first order system least squares method for the Helmholtz equation ⋮ Peter Monk's contributions to numerical analysis and Maxwell's equations ⋮ An \textit{hp}-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem ⋮ A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media ⋮ Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions ⋮ \(hp\)-adaptive finite elements in electromagnetics ⋮ Special issue: Papers of the symposium on Advances in computational mechanics, Austin, TX, USA, January 12--15, 1997. Vol. 5 ⋮ Overlapping solution finite element method-higher order approximation and implementation ⋮ Error estimates and adaptive finite element methods ⋮ Whitney forms and their extensions ⋮ Hierachic \(hp\)-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes ⋮ A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

Uses Software

• TRIFOU

Cites Work

• Unnamed Item
• Unnamed Item
• The p- and h-p versions of the finite element method. An overview
• Mixed finite elements in \(\mathbb{R}^3\)
• Éléments finis mixtes incompressibles pour l'équation de Stokes dans \(R^ 3\).
• A finite element method for approximating the time-harmonic Maxwell equations
• On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation
• Finite Element Methods for Navier-Stokes Equations
• A Mixed Method for Approximating Maxwell’s Equations
• Eigenvalue Approximation by a Mixed Method for Resonant Inhomogeneous Cavities with Metallic Boundaries
• Mixed finite element methods for quasilinear second order elliptic problems : the $p$-version
• On the Stability and Convergence of Higher-Order Mixed Finite Element Methods for Second-Order Elliptic Problems