Uniform preconditioners for problems of positive order. (15th June 2020)

• Record Type: Journal Article
• Authors: Stevenson, Rob; van Venetië, Raymond
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 12(2020)
• Page Start: 3516
• Page End: 3530
• Publication Date: 2020-06-15
• Subjects: Operator preconditioning -- Uniform preconditioners -- Finite- and boundary elements; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.02.009
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Using the framework of operator or Caldéron preconditioning, uniform preconditioners are constructed for elliptic operators of order 2 s ∈ [ 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.