Uniform convergence of a weak Galerkin method for singularly perturbed convection–diffusion problems

Jin Zhang and Xiaowei Liu

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 200, issue C, 393-403

Abstract: In this article, we analyze convergence of a weak Galerkin method on Bakhvalov-type mesh. This method uses piecewise polynomials of degree k≥1 on the interior and piecewise constant on the boundary of each element. To obtain uniform convergence, we carefully define the penalty parameter and a new interpolant which is based on the characteristic of the Bakhvalov-type mesh. Then the method is proved to be convergent with optimal order, which is confirmed by numerical experiments.

Keywords: Singular perturbation; Convection–diffusion equation; Bakhvalov-type mesh; Weak Galerkin method (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:200:y:2022:i:c:p:393-403

DOI: 10.1016/j.matcom.2022.04.023

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