@article{Shi2024, 
author = {Yang Shi and Xuehua Yang},
title = {Pointwise error estimate of conservative difference scheme for supergeneralized viscous Burgers' equation},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {3},
pages = {1471-1497},
keywords = {supergeneralized viscous Burgers' equation, finite difference method, conservativity, pointwise error estimate, convergence},
url = {https://www.sciopen.com/article/10.3934/era.2024068},
doi = {10.3934/era.2024068},
abstract = {This work focuses on exploring pointwise error estimate of three-level conservative difference scheme for supergeneralized viscous Burgers' equation. The cut-off function method plays an important role in constructing difference scheme and presenting numerical analysis. We study the conservative invariant of proposed method, which is energy-preserving for all positive integers    p and    q. Meanwhile, one could apply the discrete energy argument to the rigorous proof that the three-level scheme has unique solution combining the mathematical induction. In addition, we prove the        L    2  -norm and        L          ∞      -norm convergence of proposed scheme in pointwise sense with separate and different ways, which is different from previous work in [1]. Numerical results verify the theoretical conclusions.}
}