A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes

Suayip Toprakseven; Seza Dinibutun; Suayip Toprakseven; Seza Dinibutun

doi:10.3934/era.2024232

Electronic Research Archive

2024, Volume 32, Issue 8: 5033-5066. doi: 10.3934/era.2024232

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A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes

Suayip Toprakseven ^{1
,
,},
Seza Dinibutun ²

1.
Department of Mathematics, Yozgat Bozok University, Yozgat, Turkey
2.
Department of Mathematics and Natural Sciences, International University of Kuwait, Ardiya, Kuwait

Received: 17 July 2024 Revised: 17 August 2024 Accepted: 19 August 2024 Published: 22 August 2024

In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings.
- time dependent singularly perturbed problem,
- weak Galerkin method,
- semi-discrete and fully discrete schemes,
- layer-adapted-meshes
Citation: Suayip Toprakseven, Seza Dinibutun. A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes[J]. Electronic Research Archive, 2024, 32(8): 5033-5066. doi: 10.3934/era.2024232

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Abstract

In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings.

References

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