(Peer-Reviewed) A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations
Guanrong Li 李观荣 ¹, Yanping Chen 陈艳萍 ², Yunqing Huang 黄云清 ³
¹ School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, Guangdong, P.R. China
广东 湛江 岭南师范大学数学与统计学院
² School of Mathematical Science, South China Normal University, Guangzhou 510631, Guangdong, P.R. China
中国 广东 广州 华南师范大学数学科学学院
³ Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, P.R. China
中国 湖南 湘潭 湘潭大学数学与计算科学学院 科学工程计算与数值仿真湖南省重点实验室
Abstract
In this paper, a robust modified weak Galerkin (MWG) finite element method for reaction-diffusion equations is proposed and investigated. An advantage of this method is that it can deal with the singularly perturbed reaction-diffusion equations. Another advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries freedom.
It is worth pointing out that, in our method, the test functions space is the same as the finite element space, which is helpful for the error analysis. Optimalorder error estimates are established for the corresponding numerical approximation in various norms. Some numerical results are reported to confirm the theory.
Ultrafast all-optical modulation of wide-bandwidth pulses enabled by silicon-metasurfaces
Kaloyan Georgiev, Khosro Zangeneh Kamali, Anton A. Trifonov, Giulia Crotti, Lyuben Petrov, Stefan Georgiev, Hristo Iliev, Lei Xu, Unai Arregui Leon, Mohsen Rahmani, Giuseppe Della Valle, Ivan Buchvarov, Dragomir Neshev
Opto-Electronic Advances
2026-09-15
Physics-informed neural fields enable blind aberration correction for partially coherent quantitative phase imaging
Shun Zhou, Xingyu Huang, Linpeng Lu, Habib Ullah, Kaiyu Du, Maciej Trusiak, Malgorzata Kujawinska, Yuzhen Zhang, Yao Fan, Qian Chen, Qinrong Zhang, Chao Zuo
Opto-Electronic Science
2026-08-26
Heterogeneously integrated micro-ring with SnS₂ for dual-functional optical modulation and photodetection
Jinyi Du, Lidan Lu, Xu Zhang, Bofei Zhu, Wenbo Bo, Yingjie Xu, Guang Chen, Yanlin He, Guanghui Ren, Xiaoping Lou, Zheng You, Lianqing Zhu
Opto-Electronic Advances
2026-08-25
Hardware-aware lightweight photonic spiking neural network for pattern classification
Shuiying Xiang, Yahui Zhang, Shangxuan Shi, Haowen Zhao, Dianzhuang Zheng, Xingxing Guo, Yanan Han, Ye Tian, Liyue Zhang, Yuechun Shi, Yue Hao
Opto-Electronic Advances
2026-08-25
PhyspeNet: An empirical physics-aware network for adaptive speckle reconstructive spectrometry
Junrui Liang, Min Jiang, Jun Li, Zhongming Huang, Junhong He, Yanting Guo, Yanzhao Ke, Jun Ye, Jiangming Xu, Jinyong Leng, Pu Zhou
Opto-Electronic Advances
2026-08-25
A 36 × 240 Gbps hybrid mode/wavelength division multiplexing transmitter using lithium niobate on insulator
Mingyu Zhu, Weihan Wang, Ruitao Ma, Aoyun Gao, Chun Gao, Zexu Wang, Fei Huang, Zhenyuan Bao, Dajian Liu, Jiaxuan Gan, Zejie Yu, Huan Li, Weike Zhao, Daoxin Dai
Opto-Electronic Advances
2026-08-25
