| 1 | Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem显示文摘This paper concerns a discontinuous Galerkin(DG)method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations.We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework.The convergence rate is valid independent of the small parameter.Furthermore,we establish a sharper L^(2)-error estimate if the true solution has a special regular component.Numerical experiments are also given. | SHI Jiamin LU Zhongshu ZHANG Luyi LU Sunjia CHENG Yao | 2023 | Wuhan University Journal of Natural Sciences2023，28，5： | 0 |
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