For singularly perturbed convection-diffusion problems, supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes, especially in the case of 2D. The difficulties arise from the width of the mesh in the layer adjacent to the transition point, resulting in a suboptimal estimate for convergence. Existing analysis techniques cannot handle these difficulties well. To fill this gap, here a novel interpolation is designed delicately for the smooth part of the solution, bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method. Our theoretical result is uniform in the singular perturbation parameter $\varepsilon$ and is supported by the numerical experiments.
Chunxiao ZHANG
,
Jin ZHANG
. THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D[J]. Acta mathematica scientia, Series B, 2024
, 44(4)
: 1572
-1593
.
DOI: 10.1007/s10473-024-0421-7
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