Uniform preconditioners for problems of positive order

Using the framework of operator or Calderon preconditioning, uniform preconditioners are constructed for elliptic operators of order 2s is an element of [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. (C) 2020 Elsevier Ltd. All rights reserved.