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Volume 18, Issue 1
Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance

Jingrun Chen, Xuhong Liu, Jiangqiong Mao & Wei Yang

DOI: 10.4208/aamm.OA-2024-0069

Adv. Appl. Math. Mech., 18 (2026), pp. 11-36.

Published online: 2025-10

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  • Abstract

In this paper, we present the design of a posteriori error estimator for the plasmon phenomenon on the graphene surface and propose a method to achieve local high-precision numerical calculations when plasmon phenomena occur on the graphene surface. We provide a lower bound estimate for the posteriori error estimator, along with a proof of convergence. Specifically, the constructed posterior error estimator enables local refinement in regions where the error is significant at the graphene interface. Firstly, we outline the construction of the posterior error estimator and provide the proof of its lower bound. Secondly, we establish the convergence of the Adaptive Edge Finite Element Method (AEFEM). Finally, we present numerical results that validate the effectiveness of the error estimator.

  • Keywords

Surface plasmon phenomenon, time-harmonic Maxwell’s equations, AEFEM, residual type posteriori error estimator.

  • AMS Subject Headings

35R30, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-18-11, author = {Chen , JingrunLiu , XuhongMao , Jiangqiong and Yang , Wei}, title = {Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {18}, number = {1}, pages = {11--36}, abstract = {

In this paper, we present the design of a posteriori error estimator for the plasmon phenomenon on the graphene surface and propose a method to achieve local high-precision numerical calculations when plasmon phenomena occur on the graphene surface. We provide a lower bound estimate for the posteriori error estimator, along with a proof of convergence. Specifically, the constructed posterior error estimator enables local refinement in regions where the error is significant at the graphene interface. Firstly, we outline the construction of the posterior error estimator and provide the proof of its lower bound. Secondly, we establish the convergence of the Adaptive Edge Finite Element Method (AEFEM). Finally, we present numerical results that validate the effectiveness of the error estimator.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2024-0069}, url = {http://global-sci.org/intro/article_detail/aamm/24517.html} }
TY - JOUR T1 - Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance AU - Chen , Jingrun AU - Liu , Xuhong AU - Mao , Jiangqiong AU - Yang , Wei JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 11 EP - 36 PY - 2025 DA - 2025/10 SN - 18 DO - http://doi.org/10.4208/aamm.OA-2024-0069 UR - https://global-sci.org/intro/article_detail/aamm/24517.html KW - Surface plasmon phenomenon, time-harmonic Maxwell’s equations, AEFEM, residual type posteriori error estimator. AB -

In this paper, we present the design of a posteriori error estimator for the plasmon phenomenon on the graphene surface and propose a method to achieve local high-precision numerical calculations when plasmon phenomena occur on the graphene surface. We provide a lower bound estimate for the posteriori error estimator, along with a proof of convergence. Specifically, the constructed posterior error estimator enables local refinement in regions where the error is significant at the graphene interface. Firstly, we outline the construction of the posterior error estimator and provide the proof of its lower bound. Secondly, we establish the convergence of the Adaptive Edge Finite Element Method (AEFEM). Finally, we present numerical results that validate the effectiveness of the error estimator.

Chen , JingrunLiu , XuhongMao , Jiangqiong and Yang , Wei. (2025). Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance. Advances in Applied Mathematics and Mechanics. 18 (1). 11-36. doi:10.4208/aamm.OA-2024-0069
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