Uniform preconditioners for problems of positive order

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

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2020-06, Vol.79 (12), p.3516-3530
Main Authors: Stevenson, Rob, van Venetië, Raymond
Format: Article
Language:English
Subjects:
Finite- and boundary elements
Operator preconditioning
Uniform preconditioners
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Summary:Using the framework of operator or Caldéron preconditioning, uniform preconditioners are constructed for elliptic operators of order 2s∈[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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2020.02.009