Construction and application of algebraic dual polynomial representations for finite element methods on quadrilateral and hexahedral meshes

DOI10.1016/j.camwa.2020.09.022zbMath1493.65206arXiv1712.09472OpenAlexW3096278902MaRDI QIDQ2034891

Yanyan Li

Publication date: 23 June 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09472

zbMATH Keywords

finite element methodspectral element methodeigenvalue problemPoisson problemde Rham sequencealgebraic dual representations

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) General topics in linear spectral theory for PDEs (35P05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Differential forms in global analysis (58A10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Cites Work

• Unnamed Item
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• Breaking spaces and forms for the DPG method and applications including Maxwell equations
• Mimetic finite difference method
• Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
• Least-squares finite element methods
• Manifolds, tensor analysis, and applications.
• Spline approximation by quasiinterpolants
• Theory and practice of finite elements.
• Construction of dual bases
• A conservative hybrid method for Darcy flow
• Dual and approximate dual basis functions for B-splines and NURBS -- comparison and application for an efficient coupling of patches with the isogeometric mortar method
• Construction of dual \(B\)-spline functions
• Transfinite element methods: Blending-function interpolation over arbitrary curved element domains
• A spectral mimetic least-squares method
• A multiscale mortar multipoint flux mixed finite element method
• Finite element approximation of eigenvalue problems
• Dual Compatible Splines on Nontensor Product Meshes
• Edge Functions for Spectral Element Methods
• Finite elements in computational electromagnetism
• Finite element exterior calculus: from Hodge theory to numerical stability
• Finite Element Methods for Navier-Stokes Equations
• A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
• Matrix Preconditioning Techniques and Applications
• EDGE ELEMENT COMPUTATION OF MAXWELL'S EIGENVALUES ON GENERAL QUADRILATERAL MESHES
• The Mathematical Theory of Finite Element Methods

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