Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, we present the design of a posteriori error estimator for theplasmon phenomenon on the graphene surface and propose a method to achievelocal high-precision numerical calculations when plasmon phenomena occur on thegraphene 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 thegraphene interface. Firstly, we outline the construction of the posterior error estimator and provide the proof of its lower bound. Secondly, we establish the convergenceof the Adaptive Edge Finite Element Method (AEFEM). Finally, we present numericalresults that validate the effectiveness of the error estimator.