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A Comparison of Dual Lagrange Multiplier Spaces for Mortar Finite Element Discretizations

Published online by Cambridge University Press:  15 January 2003

Barbara I. Wohlmuth
Barbara I. Wohlmuth*
Affiliation:
Math. Institut, Universität Stuttgart, Pfaffenwaldring 57, 70 569 Stuttgart, Germany. [email protected].
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Abstract

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We focus on mortar finite element methods on non-matching triangulations. In particular, we discuss and analyze dual Lagrange multiplier spaces for lowest order finite elements. These non standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. As a consequence, standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconforming situation. Here, we introduce new dual Lagrange multiplier spaces. We concentrate on the construction of locally supported and continuous dual basis functions. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.

Keywords

Mortar finite elementsdual spacenon-matching triangulationsmultigrid methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 995 - 1012
Copyright
© EDP Sciences, SMAI, 2002

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References

Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuß, N., Rentz-Reichert, H. and Wieners, C., UG - a flexible software toolbox for solving partial differential equations. Comput. Vis. Sci. 1 (1997) 27-40. CrossRef
Braess, D. and Dahmen, W., Stability estimates of the mortar finite element method for 3-dimensional problems. East-West J. Numer. Math. 6 (1998) 249-263.
Ben Belgacem, F., The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173-197. CrossRef
Ben Belgacem, F. and Maday, Y., The mortar element method for three dimensional finite elements. RAIRO Modél. Math. Anal. Numér. 31 (1997) 289-302. CrossRef
C. Bernardi, Y. Maday and A.T. Patera, Domain decomposition by the mortar element method, in: Asymptotic and numerical methods for partial differential equations with critical parameters, H. Kaper et al. Eds., Reidel, Dordrecht (1993) 269-286.
C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in: Nonlinear partial differential equations and their applications, H. Brezzi et al. Eds., Paris (1994) 13-51.
L. Cazabeau, C. Lacour and Y. Maday, Numerical quadratures and mortar methods, in: Computational science for the 21st century. Dedicated to Prof. Roland Glowinski on the occasion of his 60th birthday. Symposium, Tours, France, May 5-7, 1997, John Wiley & Sons Ltd. (1997) 119-128.
Kim, C., Lazarov, R.D., Pasciak, J.E. and Vassilevski, P.S., Multiplier spaces for the mortar finite element method in three dimensions. SIAM J. Numer. Anal. 39 (2001) 519-538. CrossRef
Krause, R.H. and Wohlmuth, B.I., Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000) 177-206.
Y. Maday, F. Rapetti and B.I. Wohlmuth, The influence of quadrature formulas in 3d mortar methods. Lect. Notes Comput. Sci. Eng. 22 , Springer-Verlag (2002).
P. Oswald and B. Wohlmuth, On polynomial reproduction of dual FE bases, in: Thirteenth Int. Conf. on Domain Decomposition Methods (2002) 85-96.
Wohlmuth, B.I. and Krause, R.H., Multigrid methods based on the unconstrained product space arising from mortar finite element discretizations. SIAM J. Numer. Anal. 39 (2001) 192-213. CrossRef
Wohlmuth, B.I., A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989-1012. CrossRef
B.I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition. Lecture Notes in Comput. Sci. 17 , Springer, Heidelberg (2001).