@article{Toprakseven2024, 
author = {Suayip Toprakseven and Seza Dinibutun},
title = {A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {8},
pages = {5033-5066},
keywords = {time dependent singularly perturbed problem, weak Galerkin method, semi-discrete and fully discrete schemes, layer-adapted-meshes},
url = {https://www.sciopen.com/article/10.3934/era.2024232},
doi = {10.3934/era.2024232},
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.}
}