Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Uniform preconditioners for problems of negative order


Authors: Rob Stevenson and Raymond van Venetië
Journal: Math. Comp. 89 (2020), 645-674
MSC (2010): Primary 65F08, 65N38, 65N30, 45Exx
DOI: https://doi.org/10.1090/mcom/3481
Published electronically: August 23, 2019
MathSciNet review: 4044445
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

Abstract: Uniform preconditioners for operators of negative order discretized by (dis)continuous piecewise polynomials of any order are constructed from a boundedly invertible operator of opposite order discretized by continuous piecewise linears. Besides the cost of the application of the latter discretized operator, the other cost of the preconditioner scales linearly with the number of mesh cells. Compared to earlier proposals, the preconditioner has the following advantages: It does not require the inverse of a non-diagonal matrix; it applies without any mildly grading assumption on the mesh; and it does not require a barycentric refinement of the mesh underlying the trial space.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65F08, 65N38, 65N30, 45Exx

Retrieve articles in all journals with MSC (2010): 65F08, 65N38, 65N30, 45Exx


Additional Information

Rob Stevenson
Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
Email: r.p.stevenson@uva.nl

Raymond van Venetië
Affiliation: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
Email: r.vanvenetie@uva.nl

DOI: https://doi.org/10.1090/mcom/3481
Keywords: Uniform preconditioners, operators of negative order, finite and boundary elements
Received by editor(s): March 14, 2018
Received by editor(s) in revised form: September 24, 2018, and April 5, 2019
Published electronically: August 23, 2019
Additional Notes: This work was initiated during the trimester programme “Multiscale Problems: Algorithms, Numerical Analysis and Computation” January-April 2017 at the Hausdorff Research Institute for Mathematics, Bonn, Germany, whose support is gratefully acknowledged by the first author. In addition, he has been supported by NSF Grant DMS 1720297.
The second author has been supported by the Netherlands Organization for Scientific Research (NWO) under contract. no. 613.001.652
Article copyright: © Copyright 2019 American Mathematical Society