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

 

Biorthogonal bases with local support and approximation properties


Authors: Bishnu P. Lamichhane and Barbara I. Wohlmuth
Journal: Math. Comp. 76 (2007), 233-249
MSC (2000): Primary 65N30, 65N55, 65D32
Published electronically: October 11, 2006
MathSciNet review: 2261019
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree $ p$ in one dimension. In contrast to earlier approaches, these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree $ p-1$. Working with Gauß-Lobatto nodes, we find an interesting connection between biorthogonality and quadrature formulas. One important application of these newly constructed biorthogonal basis functions are two-dimensional mortar finite elements. The weak continuity condition of the constrained mortar space is realized in terms of our new dual bases. As a result, local static condensation can be applied which is very attractive from the numerical point of view. Numerical results are presented for cubic mortar finite elements.


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Additional Information

Bishnu P. Lamichhane
Affiliation: Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany
Email: lamichhane@mathematik.uni-stuttgart.de

Barbara I. Wohlmuth
Affiliation: Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, Germany
Email: wohlmuth@mathematik.uni-stuttgart.de

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01907-7
PII: S 0025-5718(06)01907-7
Keywords: Biorthogonal basis, domain decomposition, Lagrange multipliers, reproduction property
Received by editor(s): April 7, 2005
Received by editor(s) in revised form: October 20, 2005
Published electronically: October 11, 2006
Additional Notes: This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12.
Article copyright: © Copyright 2006 American Mathematical Society