Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD)

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Cai, Wei, et al. “Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD)”. Communications in Mathematics and Statistics, vol. 1, no. 1, 2013, pp. 19-35, https://doi.org/10.1007/s40304-013-0003-9.
Cai, W., Wu, J., & Xin, J. (2013). Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD). Communications in Mathematics and Statistics, 1(1), 19-35. https://doi.org/10.1007/s40304-013-0003-9
Cai, Wei, Jian Wu, and Jianguo Xin. “Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD)”. Communications in Mathematics and Statistics 1, no. 1 (2013): 19-35. https://doi.org/10.1007/s40304-013-0003-9.
1.
Cai W, Wu J, Xin J. Divergence-Free $\boldsymbol{\mathcal{H}}(\mathbf{div})$ -Conforming Hierarchical Bases for Magnetohydrodynamics (MHD). Communications in Mathematics and Statistics. 2013;1(1):19-35.
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Mathematics
Refrences
Title Journal Journal Categories Citations Publication Date
On the Construction of Well-Conditioned Hierarchical Bases for (div)-Conforming ℝn Simplicial Elements

 Communications in Computational Physics
  • Science: Mathematics
  • Science: Physics
 6 2013
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra Numerische Mathematik
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 63 2012
Mixed finite element methods for general quadrilateral grids Applied Mathematics and Computation
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 5 2011
HexahedralH(div) andH(curl) finite elements ESAIM: Mathematical Modelling and Numerical Analysis
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
 35 2011
A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics Computer Methods in Applied Mechanics and Engineering
  • Technology: Engineering (General). Civil engineering (General)
  • Science: Mathematics
  • Technology: Engineering (General). Civil engineering (General): Mechanics of engineering. Applied mechanics
  • Technology: Mechanical engineering and machinery
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
 107 2010
Refrences Analysis
Category Category Repetition
Science: Mathematics11
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods5
Technology: Engineering (General). Civil engineering (General)4
Science: Mathematics: Instruments and machines: Electronic computers. Computer science3
Science: Physics3
Science: Astronomy3
Science: Astronomy: Astrophysics1
Technology: Engineering (General). Civil engineering (General): Mechanics of engineering. Applied mechanics1
Technology: Mechanical engineering and machinery1
The category Science: Mathematics 11 is the most frequently represented among the references in this article. It primarily includes studies from Numerische Mathematik and Journal of Computational Physics. The chart below illustrates the number of referenced publications per year.
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Citations
Title Journal Journal Categories Citations Publication Date
Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations

 Numerical Methods for Partial Differential Equations
  • Science: Mathematics
  • Technology: Engineering (General). Civil engineering (General)
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Technology: Engineering (General). Civil engineering (General)
 2023
An efficient construction of divergence-free spaces in the context of exact finite element de Rham sequences Computer Methods in Applied Mechanics and Engineering
  • Technology: Engineering (General). Civil engineering (General)
  • Science: Mathematics
  • Technology: Engineering (General). Civil engineering (General): Mechanics of engineering. Applied mechanics
  • Technology: Mechanical engineering and machinery
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
 1 2022
Uniform Stability and Convergence with Respect to $$(\nu , \mu , s, 1-\sigma )$$ of the Three Iterative Finite Element Solutions for the 3D Steady MHD Equations Journal of Scientific Computing
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 7 2021
A Convergent Linearized Lagrange Finite Element Method for the Magneto-hydrodynamic Equations in Two-Dimensional Nonsmooth and Nonconvex Domains SIAM Journal on Numerical Analysis
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2020
A graph approach for the construction of high order divergence-free Raviart–Thomas finite elements Calcolo
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 3 2018
Citations Analysis
Category Category Repetition
Science: Mathematics10
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods9
Technology: Engineering (General). Civil engineering (General)3
Science: Mathematics: Instruments and machines: Electronic computers. Computer science2
Technology: Engineering (General). Civil engineering (General): Mechanics of engineering. Applied mechanics1
Technology: Mechanical engineering and machinery1
The category Science: Mathematics 10 is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Spectral Method For Navier–Stokes Equations With Non-slip Boundary Conditions By Using Divergence-Free Base Functions and was published in 2015. The most recent citation comes from a 2023 study titled Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations. This article reached its peak citation in 2018, with 2 citations. It has been cited in 8 different journals. Among related journals, the Journal of Scientific Computing cited this research the most, with 4 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year