TY - JOUR
T1 - Convergence of a Discontinuous Galerkin Method on Bakhvalov-Type Meshes for Singularly Perturbed Volterra Integro-Differential Equations
AU - Liao , Yige
AU - Luo , Xianbing
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 770
EP - 786
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2024-075.140824
UR - https://global-sci.org/intro/article_detail/eajam/24196.html
KW - Singularly perturbed, Bakhvalov mesh, discontinuous Galerkin, parameter-uniform convergence.
AB - <p style="text-align: justify;">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.</p>