中文摘要：

本文针对常系数和变系数两点混合边值问题提出一种紧有限体积格式,该格式形成的线性代数方程组具有三对角性质,可以使用追赶法求解.证明格式按照H1半范数具有四阶收敛精度.利用节点计算值,给出单元中点值和一阶导数值的高精度后处理计算公式,这两个公式同样具有四阶精度.数值算例验证了理论分析的正确性,并说明了格式的有效性.

英文摘要：

In this paper,a compact finite volume scheme is proposed for mixed two point boundary value problems with both constant coefficient and variable coefficient.The linear algebraic system derived by this scheme has tridiagonal property and can be solved by Thomas method.It is proved that the given scheme is convergent with fourth-order accuracy according to H1 discrete seminorm.Furthermore,the post-processing formulas for the numerical value and derivative at midpoint of every element are obtained,which both have fourth order accuracy.Numerical examples verify the correctness of the theoretical analysis and also show the effectiveness of the scheme.