Optimal order of uniform convergence for finite element method on Bakhvalov-type meshes

2020/02/28 by Jin Zhang, Xiaowei Liu, Zhang, Jin +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #cs.NA #math.NA #msc:65N12 #msc:65N30 #msc:65N50

paper · pdf · doi:10.48550/arxiv.2003.10219

12pages

arxiv created 2020/02/28 · arxiv updated 2020/03/24

Abstract

We propose a new analysis of convergence for a kth order (k≥ 1) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has a simple structure and is easy to generalize. By means of this interpolant, we prove an optimal order of uniform convergence with respect to the perturbation parameter. Numerical experiments illustrate these theoretical results.

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