Uniform 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

DOI:
https://doi.org/10.1090/S0025-5718-99-01083-2

Published electronically:
February 26, 1999

MathSciNet review:
1642762

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Abstract | References | Similar Articles | Additional Information

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 or 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 version is used. Numerical results for and mortar FEMs show that these methods behave as well as conforming FEMs. An 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:
https://doi.org/10.1090/S0025-5718-99-01083-2

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