# A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations

- Volume: 36, Issue: 6, page 995-1012
- ISSN: 0764-583X

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topWohlmuth, Barbara I.. "A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.6 (2002): 995-1012. <http://eudml.org/doc/244915>.

@article{Wohlmuth2002,

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.},

author = {Wohlmuth, Barbara I.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Mortar finite elements; dual space; non-matching triangulations; multigrid methods; mortar finite elements; second-order elliptic boundary value problem; domain decomposition; dual Lagrange multiplier spaces; numerical results},

language = {eng},

number = {6},

pages = {995-1012},

publisher = {EDP-Sciences},

title = {A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations},

url = {http://eudml.org/doc/244915},

volume = {36},

year = {2002},

}

TY - JOUR

AU - Wohlmuth, Barbara I.

TI - A comparison of dual Lagrange multiplier spaces for Mortar finite element discretizations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2002

PB - EDP-Sciences

VL - 36

IS - 6

SP - 995

EP - 1012

AB - 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.

LA - eng

KW - Mortar finite elements; dual space; non-matching triangulations; multigrid methods; mortar finite elements; second-order elliptic boundary value problem; domain decomposition; dual Lagrange multiplier spaces; numerical results

UR - http://eudml.org/doc/244915

ER -

## References

top- [1] P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuß, H. Rentz–Reichert and C. Wieners, UG – a flexible software toolbox for solving partial differential equations. Comput. Vis. Sci. 1 (1997) 27–40. Zbl0970.65129
- [2] D. Braess and W. Dahmen, Stability estimates of the mortar finite element method for 3–dimensional problems. East-West J. Numer. Math. 6 (1998) 249–263. Zbl0922.65072
- [3] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–197. Zbl0944.65114
- [4] F. Ben Belgacem and Y. Maday, The mortar element method for three dimensional finite elements. RAIRO Modél. Math. Anal. Numér. 31 (1997) 289–302. Zbl0868.65082
- [5] 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. Zbl0799.65124
- [6] 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. Zbl0797.65094
- [7] 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. Zbl0911.65117
- [8] C. Kim, R.D. Lazarov, J.E. Pasciak and P.S. Vassilevski, Multiplier spaces for the mortar finite element method in three dimensions. SIAM J. Numer. Anal. 39 (2001) 519–538. Zbl1006.65129
- [9] R.H. Krause and B.I. Wohlmuth, Nonconforming domain decomposition techniques for linear elasticity. East-West J. Numer. Math. 8 (2000) 177–206. Zbl1050.74046
- [10] 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). Zbl1007.65096MR1962690
- [11] P. Oswald and B. Wohlmuth, On polynomial reproduction of dual FE bases, in: Thirteenth Int. Conf. on Domain Decomposition Methods (2002) 85–96. Zbl1026.65098
- [12] B.I. Wohlmuth and R.H. Krause, Multigrid methods based on the unconstrained product space arising from mortar finite element discretizations. SIAM J. Numer. Anal. 39 (2001) 192–213. Zbl0992.65142
- [13] B.I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989–1012. Zbl0974.65105
- [14] B.I. Wohlmuth, Discretization methods and iterative solvers based on domain decomposition. Lecture Notes in Comput. Sci. 17, Springer, Heidelberg (2001). Zbl0966.65097MR1820470

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