Using the framework of operator or Caldéron preconditioning, uniform preconditioners are constructed for elliptic operators of order $2s\in [0,2]$ discretized with continuous finite (or boundary) elements. The cost of the preconditioner is the cost of the application an elliptic opposite order operator discretized with discontinuous or continuous finite elements on the same mesh, plus minor cost of linear complexity. Herewith the construction of a so-called dual mesh is avoided.

中文翻译：

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一致的前置条件，用于解决正序问题

使用运算符或Caldéron预处理的框架，为阶椭圆运算符构造统一的预处理器 $2s\in [0，2]$用连续有限（或边界）元素离散化。预处理器的成本是应用椭圆形相反阶运算符的成本，该椭圆形反序算子在同一网格上离散有不连续或连续的有限元，加上线性复杂度的较小成本。因此，避免了所谓的双重网格的构造。