East Asian J. Appl. Math., 15 (2025), pp. 770-786.
Published online: 2025-06
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2024-075.140824}, url = {http://global-sci.org/intro/article_detail/eajam/24196.html} }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.