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

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_{\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.

Keywords

• supergeneralized viscous burgers' equation
• finite difference method
• conservativity
• pointwise error estimate
• convergence