We focus on studying supercloseness of linear finite element method on Bakhvalov-type triangular meshes for a singularly perturbed convection-diffusion problem. To achieve the optimal supercloseness result, we introduce a novel interpolation with a simplified structure that is specially designed for the exponential layer part of the solution. This new interpolation is constructed based on the inherent characteristics of the exponential layer function and the structures of Bakhvalov-type triangular meshes. Note that some boundary corrections should be carefully defined to guarantee the homogeneous Dirichlet boundary condition. Furthermore, some integral inequalities also assume a crucial role in our analysis. Finally, supercloseness of almost 3/2th order can be obtained on Bakhvalov-type triangular meshes. This parameter-uniform convergence result is considered optimal for triangular meshes and is supported by numerical experiments.
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页码:243 / 253
页数:11
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Benzi M, 2005, ACTA NUMER, V14, P1, DOI 10.1017/S0962492904000212
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Univ Novi Sad, Fac Sci, Dept Math & Informat, Trg Dositeja Obradovica 4, Novi Sad 21000, SerbiaUniv Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia
Radojev, G.
Roos, H-G
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Tech Univ Dresden, Inst Numer Math, D-01062 Dresden, GermanyUniv Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia
Roos, H-G
Teofanov, Lj
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Univ Novi Sad, Fac Tech Sci, Trg Dositeja Obradovica 6, Novi Sad 21000, SerbiaUniv Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia
机构:
Univ Novi Sad, Fac Sci, Dept Math & Informat, Trg Dositeja Obradovica 4, Novi Sad 21000, SerbiaUniv Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia
Radojev, G.
Roos, H-G
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h-index: 0
机构:
Tech Univ Dresden, Inst Numer Math, D-01062 Dresden, GermanyUniv Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia
Roos, H-G
Teofanov, Lj
论文数: 0引用数: 0
h-index: 0
机构:
Univ Novi Sad, Fac Tech Sci, Trg Dositeja Obradovica 6, Novi Sad 21000, SerbiaUniv Novi Sad, Fac Technol, Bulevar Cara Lazara 1, Novi Sad 21000, Serbia