Summary
Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We consider mortar techniques with dual Lagrange multiplier spaces to couple different discretization schemes. It is well known that the discretization error for linear mortar finite elements in the energy norm is of order h. Here, we apply these techniques to curvilinear boundaries, nonlinear problems and the coupling of different model equations and discretizations.
Keywords
- Lagrange Multiplier
- Discretization Error
- Incompressible Material
- Mortar Method
- Domain Decomposition Technique
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12.
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References
A. Alonso, A. D. Russo, C. Otero-Souto, C. Padra, and R. Rodríguez. An adaptive finite element scheme to solve fluid-structure vibration problems on non-matching grids. Computing and Visualization in Science, 4:67–78, 2001.
C. Atkinson and C. R. Champion. Some boundary-value problems for the equation ▽ · (|▽ø |N) = 0. Quart. J. Mech. Appl. Math., 37:401–419, 1984.
I. Babuška and M. Suri. On locking and robustness in the finite element method. SIAM J. Numer. Anal., 29:1261–1293, 1992.
A. Bermúdez, R. Duran, M. Muschietti, R. Rodríguez, and J. Solomin. Finite element vibration analysis of fluid-solid systems without spurious modes. SIAM J. Numer. Anal., 32:1280–1295, 1995.
A. Bermúdez and R. Rodríguez. Finite element computation of the vibration modes of a a fluid-solid system. Comput. Meth. in Appl. Mech. and Engrg., 119:355–370, 1994.
C. Bernardi, Y. Maday, and A. Patera. Domain decomposition by the mortar element method. In H. K. et al., editor, Asymptotic and numerical methods for partial differential equations with critical parameters, pages 269–286. Reidel, Dordrecht, 1993.
C. Bernardi, Y. Maday, and A. Patera. A new nonconforming approach to domain decomposition: the mortar element method. In H. B. et al., editor, Nonlinear partial differential equations and their applications, pages 13–51. Paris, 1994.
D. Braess. Finite Elements. Theory, fast solver, and applications in solid mechanics. Cambridge Univ. Press, Second Edition, 2001.
P. Hansbo and J. Hermansson. Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems. Comput. Mech., 32:134–139, 2003.
W. Liu. Degenerate quasilinear elliptic equations arising from bimaterial problems in elastic-plastic mechanics. Nonlinear Analysis, 35:517–529, 1999.
W. Liu and J. Barret. A remark on the regularity of the solutions of the p-Laplacian and its application. J. Math. Anal. Appl., 178:470–488, 1993.
W. Liu and N. Yan. Quasi-norm local error estimators for p-Laplacian. SIAM J. Numer. Anal., 39:100–127, 2001.
B. Wohlmuth. Discretization Methods and Iterative Solvers Based on Domain Decomposition, volume 17 of LNCS. Springer Heidelberg, 2001.
B. Wohlmuth and R. Krause. Multigrid methods based on the unconstrained product space arising from mortar finite element discretizations. SIAM J. Numer. Anal., 39:192–213, 2001.
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Lamichhane, B.P., Wohlmuth, B.I. (2005). Mortar Finite Elements with Dual Lagrange Multipliers: Some Applications. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_31
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DOI: https://doi.org/10.1007/3-540-26825-1_31
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