Superconvergence analysis of two-grid FEM for Maxwell’s equations with a thermal effect

Yao, Changhui; Li, F.R.; Zhao, Yanxing

doi:10.1016/j.camwa.2020.02.001

Cited by 8 publications

(2 citation statements)

References 26 publications

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“…Almost at the same time, Huang and Chen [15] proposed a multilevel iterative method for simulating the nonlinear singular two-point boundary value problems. Since then, TGMs have been applied to many different kinds of problems, for example, eigenvalue problems [47], nonlinear parabolic equations [9,11], mixed Stokes-Darcy models [29], nonlinear coupling miscible displacement problems [6], nonlinear elliptic interface problems [42], Maxwell's equations [48].…”

Section: Introductionmentioning

confidence: 99%

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

Nuodi Liu,

Yanping Chen,

Yunqing 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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Section: Introductionmentioning

confidence: 99%

“…Inspired by ideas of Yao et al [48], we adopt the postprocessing technique with superconvergence to improve the convergence on the coarse mesh. Generally speaking, the superconvergent solution is obtained by reconstructing a finite element solution in a higher interpolation space, so that the convergence rate is greatly improved.…”

Section: Introductionmentioning

confidence: 99%