Superconvergent recovery of edge finite element approximation for Maxwell’s equations

Wu, Chao; Huang, Yunqing; Yi, Nianyu; Yuan, Jinyun

doi:10.1016/j.cma.2020.113302

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…refs. [5,7,13,25,37,49], including superconvergence analysis for Maxwell's equations [16,20,28,41,43]. In this paper, we mainly concentrate on the TGM for solving this Cole-Cole model.…”

Section: Introductionmentioning

confidence: 99%

Two-Grid Methods for Maxwell’s Equations in a Cole-Cole Dispersive Medium

Liu,

null,

Huang

2024

EAJAM

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A two-grid method (TGM) for the time-dependent Maxwell's equations in Cole-Cole dispersive media with a fractional time derivative term is proposed. We employ the lowest Raviart-Thomas-Nédélec mixed finite elements to discrete the space. It is known that for these type of Nédélec edge finite elements, the standard TGM cannot be applied directly. Therefore, we modified the traditional TGM, and the discrete process can be divided into two steps. Firstly, we get the rough discrete solutions on the coarse mesh. At the same time, superconvergence results can be obtained by using a post-processing technique. Secondly, the superconvergent solutions on the coarse grid are added on the fine mesh as a correction, and the optimal error estimates could be obtained accordingly. Finally, the numerical experiments can verify that the theoretical results are correct and reasonable.

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“…refs. [5,7,13,25,37,49], including superconvergence analysis for Maxwell's equations [16,20,28,41,43]. In this paper, we mainly concentrate on the TGM for solving this Cole-Cole model.…”

Section: Introductionmentioning

confidence: 99%

Two-Grid Methods for Maxwell’s Equations in a Cole-Cole Dispersive Medium

Liu,

null,

Huang

2024

EAJAM

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“…Efficient numerical analysis to Maxwell equation is an important study hotspot. Numerical investigations of Maxwell equations include symplectic exponential integrator [1], compact scheme [2], Runge-Kutta method [3], stochastic Euler scheme [4], multisymplectic schemes [5][6][7][8], energy-conserving method [9], wavelet collocation method [10,11], Hamiltonian time integrators [12], finite element method [13,14], spectral method [15] and other numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions

et al. 2021

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Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy conservation laws. The scheme also preserves two discrete divergences. To reduce computation cost, we split the original Maxwell equations into three local one-dimension (LOD) Maxwell equations. Then exponentially fitted trapezoidal scheme, applied to the resulted LOD equations, generates LOD multisymplectic scheme. We prove the unconditional stability and convergence of the LOD multisymplectic scheme. Convergence of numerical dispersion relation is also analyzed. At last, we present two numerical examples with periodic oscillatory solutions to confirm the theoretical analysis. Numerical results indicate that the LOD multisymplectic scheme is efficient, stable and conservative in solving conservative Maxwell equations with oscillatory solutions. In addition, to one-dimension Maxwell equations, we apply least square method and LOD multisymplectic scheme to fit the electric permittivity by using exact solution disturbed with small random errors as measured data. Numerical results of parameter inversion fit well with measured data, which shows that least square method combined with LOD multisymplectic scheme is efficient to estimate the model parameter under small random disturbance.

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Function and Curl Recovery for the Lowest Order Triangular Edge Element

Huang²,

Yi³

et al. 2022

J Sci Comput

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Superconvergent recovery of edge finite element approximation for Maxwell’s equations

Cited by 7 publications

References 22 publications

Two-Grid Methods for Maxwell’s Equations in a Cole-Cole Dispersive Medium

Two-Grid Methods for Maxwell’s Equations in a Cole-Cole Dispersive Medium

Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions

Function and Curl Recovery for the Lowest Order Triangular Edge Element

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