Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D

2020/11/25 by Jin Zhang, Zhang, Jin, Yanhui Lv +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2011.12718

arxiv created 2020/11/25 · openalex publication_date 2020/11/25 · arxiv updated 2020/11/26 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28

Abstract

For a singularly perturbed elliptic model problem with two small parameters, we analyze finite element methods of any order on a Bakhvalov-type mesh. For convergence analysis, we construct a new interpolation by using the characteristics of layers. Besides, a more subtle analysis of the mesh scale near the exponential layer is carried out. Based on the interpolation and new analysis of the mesh scale, we prove the optimal convergence order.

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