Uniform preconditioners for problems of positive order

Abstract

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.

References in corpus (2)

• Uniform preconditioners for problems of negative order
• Closed-Form Exact Inverses of the Weakly Singular and Hypersingular Operators On Disks

Cited by in corpus (7)

• Further results on a space-time FOSLS formulation of parabolic PDEs
• Optimal operator preconditioning for pseudodifferential boundary problems
• Uniform preconditioners of linear complexity for problems of negative order
• On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
• An Auxiliary Space Preconditioner for Fractional Laplacian of Negative Order
• Operator preconditioning: the simplest case
• Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two