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.

中文翻译：

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广义粘性Burgers方程的精确解和数值解的研究

在本文中，我们回顾了精确解的一致有界性，然后研究了两种保守的数值离散方案的逐点误差估计。我们表明，对于所有正整数，两个差分方案都共享与原始连续模型相似的保守不变式$p$。特别地，我们证明了基于截止函数方法的差分方案在逐点意义上是收敛的。数值例子验证了我们的理论结果。