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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Uniform $hp$ convergence results
for the mortar finite element method


Authors: Padmanabhan Seshaiyer and Manil Suri
Journal: Math. Comp. 69 (2000), 521-546
MSC (1991): Primary 65N30, 65N15
Published electronically: February 26, 1999
MathSciNet review: 1642762
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Abstract: The mortar finite element is an example of a non-conforming method which can be used to decompose and re-compose a domain into subdomains without requiring compatibility between the meshes on the separate components. We obtain stability and convergence results for this method that are uniform in terms of both the degree and the mesh used, without assuming quasiuniformity for the meshes. Our results establish that the method is optimal when non-quasiuniform $h$ or $hp$ methods are used. Such methods are essential in practice for good rates of convergence when the interface passes through a corner of the domain. We also give an error estimate for when the $p$ version is used. Numerical results for $h,p$ and $hp$ mortar FEMs show that these methods behave as well as conforming FEMs. An $hp$ extension theorem is also proved.


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Additional Information

Padmanabhan Seshaiyer
Affiliation: Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843-3120
Email: padhu@terminator.tamu.edu

Manil Suri
Affiliation: Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250
Email: suri@math.umbc.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01083-2
PII: S 0025-5718(99)01083-2
Keywords: $p$ version, $hp$ version, mortar elements, finite elements, non-conforming
Received by editor(s): August 4, 1997
Received by editor(s) in revised form: April 7, 1998
Published electronically: February 26, 1999
Additional Notes: This work was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant F49620-95-I-0230, and by the National Science Foundation under Grant DMS-9706594.
Article copyright: © Copyright 2000 American Mathematical Society