Supercloseness of the NIPG method on Bakhvalov-type meshes for a system of singularly perturbed reaction-diffusion equations

Xiaobing Bao; Lei Xu; Yong Zhang; Xiaobing Bao; Lei Xu; Yong Zhang

doi:10.3934/nhm.2025053

Networks and Heterogeneous Media

2025, Volume 20, Issue 4: 1230-1250. doi: 10.3934/nhm.2025053

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Supercloseness of the NIPG method on Bakhvalov-type meshes for a system of singularly perturbed reaction-diffusion equations

1.
School of Big Data and Artificial Intelligence Chizhou University, Chizhou 247000, China
2.
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received: 15 August 2025 Revised: 22 October 2025 Accepted: 30 October 2025 Published: 12 November 2025

In this paper, a higher order nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov mesh is developed for a weakly coupled system of singularly perturbed reaction-diffusion equations. At first, by selecting special penalty parameters at different mesh points, the supercloseness of the $ k+\frac{1}{2} $ order of our proposed method is derived, where $ k $ is the degree of polynomials space. Then, an optimal order of uniform convergence analysis in a balanced norm is performed. Finally, some numerical experiments are given to support our theoretical findings.
- singularly perturbed,
- the NIPG method,
- Bakhvalov-type mesh,
- balanced norm,
- supercloseness
Citation: Xiaobing Bao, Lei Xu, Yong Zhang. Supercloseness of the NIPG method on Bakhvalov-type meshes for a system of singularly perturbed reaction-diffusion equations[J]. Networks and Heterogeneous Media, 2025, 20(4): 1230-1250. doi: 10.3934/nhm.2025053

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Abstract

In this paper, a higher order nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov mesh is developed for a weakly coupled system of singularly perturbed reaction-diffusion equations. At first, by selecting special penalty parameters at different mesh points, the supercloseness of the $ k+\frac{1}{2} $ order of our proposed method is derived, where $ k $ is the degree of polynomials space. Then, an optimal order of uniform convergence analysis in a balanced norm is performed. Finally, some numerical experiments are given to support our theoretical findings.

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