An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
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Publication:2119997
DOI10.1016/j.jcp.2020.109991OpenAlexW3025717014MaRDI QIDQ2119997
Jérôme Droniou, Daniele A. Di Pietro
Publication date: 31 March 2022
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.06890
Basic methods for problems in optics and electromagnetic theory (78Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)
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Cites Work
- Unnamed Item
- \(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods
- High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality
- Isogeometric analysis in electromagnetics: B-splines approximation
- Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
- Base functions and discrete constitutive relations for staggered polyhedral grids
- Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
- A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation
- Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes
- Stabilized interior penalty methods for the time-harmonic Maxwell equations.
- The hybrid high-order method for polytopal meshes. Design, analysis, and applications
- Lowest order virtual element approximation of magnetostatic problems
- A superconvergent HDG method for the Maxwell equations
- The mimetic finite difference method for elliptic problems
- Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems
- A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes
- Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems
- Isogeometric Discrete Differential Forms in Three Dimensions
- Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
- Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes
- A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics
- A Three-Dimensional Hybrid High-Order Method for Magnetostatics
- Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator
- Cohomology in 3D Magneto-Quasistatics Modeling
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