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

DOI:
https://doi.org/10.1090/S0025-5718-06-01907-7

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 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 . 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:
https://doi.org/10.1090/S0025-5718-06-01907-7

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