The study of exact and numerical solutions of the generalized viscous Burgers' equation

In the paper, we revisit the uniform boundedness of the exact solution and then study pointwise error estimate for two kinds of conservative numerical discretization schemes. We show that both difference schemes share the conservative invariants similar to the original continuous model for all positive integers p. In particular, we prove that difference schemes are convergent in pointwise sense based on the cut-off function method. A numerical example is carried out to verify our theoretical results. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper revisits the uniform boundedness of the exact solution and investigates pointwise error estimate for two types of conservative numerical discretization schemes. It is shown that both difference schemes possess conservative invariants similar to the original continuous model for all positive integers p. Particularly, the convergence of difference schemes in a pointwise sense is proved based on the cut-off function method. A numerical example is presented to validate the theoretical results.