Pointwise error estimate of conservative difference scheme for supergeneralized viscous Burgers' equation

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 $L_{\mathrm{\infty }}$-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.