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arXiv · 2305.10778

Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh

Chunxiao Zhang·Jin Zhang·Wenchao Zheng
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Abstract

In this paper, we focus on analyzing the supercloseness property of a two-dimensional singularly perturbed convection-diffusion problem with exponential boundary layers. The local discontinuous Galerkin (LDG) method with piecewise tensor-product polynomials of degree k is applied to Bakhvalov-type mesh. By developing special two-dimensional local Gauss-Radau projections and establishing a novel interpolation, supercloseness of an optimal order k+1 can be achieved on Bakhvalov-type mesh. It is crucial to highlight that this supercloseness result is independent of the singular perturbation parameter.

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Chunxiao Zhang, Jin Zhang, Wenchao Zheng. 2023-05-18. Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh. https://arxiv.org/abs/2305.10778

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