Convergence of a Discontinuous Galerkin Method on Bakhvalov-Type Meshes for Singularly Perturbed Volterra Integro-Differential Equations
Year: 2025
Author: Yige Liao, Xianbing Luo
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 4 : pp. 770–786
Abstract
A discontinuous Galerkin (DG) method on Bakhvalov-type (B-type) meshes for singularly perturbed Volterra integro-differential equations (SPVIDEs) is proposed. We derive abstract error bounds of the DG method for the SPVIDEs in the $L^2$-norm. It is shown that the approximate solution generated by the DG method on B-type meshes has optimal convergence rate $k + 1$ in the $L^2$-norm, when using the piecewise polynomial space of degree $k.$ Numerical simulations demonstrate the validity of the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2024-075.140824
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 4 : pp. 770–786
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Singularly perturbed Bakhvalov mesh discontinuous Galerkin parameter-uniform convergence.