中文摘要：

提出一个保守恒保单调的PQIM插值算子,论证该算子的收敛阶、保守恒性与保单调性,通过数值实验,证明该算子能有效地抑制可能由插值引起的振荡.

英文摘要：

We propose a monotonicity-and conservation-preserving interpolation operator,named PQIM.Its order of convergence,conservation-preserving and monotonicity-preserving properties are demonstrated.The interpolation operator is proved to restrain oscillation caused by interpolation effectively.