Convergence of a finite element method on a Bakhvalov-type mesh for singularly perturbed reaction–diffusion equation

Jin Zhang and Xiaowei Liu

Applied Mathematics and Computation, 2020, vol. 385, issue C

Abstract: A finite element method is applied on a Bakhvalov-type mesh to solve a singularly perturbed reaction–diffusion problem whose solution exhibits boundary layers. A uniform convergence order of O(N−(k+1)+ε1/2N−k) is proved, where k is the order of piecewise polynomials in the finite element method, ε is the diffusion parameter and N is the number of partitions in each direction. Numerical experiments support this theoretical result.

Keywords: Singular perturbation; Reaction–diffusion equation; Bakhvalov-type mesh; Finite element method; Higher-order; Uniform convergence (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303659

DOI: 10.1016/j.amc.2020.125403

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