Multigrid Methods for Mixed Finite Element Discretizations of Variational Inequalities

作者: Tilman Neunhoeffer

DOI: 10.1007/978-3-0348-8524-9_19

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摘要: We present a scheme for solving variational inequalities of obstacle type using mixed finite elements discretization and we show the equivalence to modified nonconforming method. This is solved suitable multigrid methods. Numerical results are given elastic-plastic torsion cylindrical bar dam problem.

参考文章(12)
R. Kornhuber, B. Erdmann, R. H. W. Hoppe, M. Frei, U. Wiest, Adaptive finite element methods for variational inequalities de Gruyter. ,(1993)
Franco Brezzi, William W. Hager, P. A. Raviart, Error estimates for the finite element solution of variational inequalities Numerische Mathematik. ,vol. 31, pp. 1- 16 ,(1978) , 10.1007/BF01396010
David Kinderlehrer, Guido Stampacchia, An introduction to variational inequalities and their applications ,(1980)
Jean Roberts, Jean-Marie Thomas, Mixed and hybrid finite element methods Springer-Verlag. ,(1991) , 10.1007/978-1-4612-3172-1
R. H. W. Hoppe, R. Kornhuber, Adaptive multilevel methods for obstacle problems SIAM Journal on Numerical Analysis. ,vol. 31, pp. 301- 323 ,(1994) , 10.1137/0731016
D. Braess, R. Verfürth, Multigrid methods for nonconforming finite element methods SIAM Journal on Numerical Analysis. ,vol. 27, pp. 979- 986 ,(1990) , 10.1137/0727056
C. Baiocchi, V. Comincioli, L. Guerri, G. Volpi, Free boundary problems in the theory of fluid flow through porous media: A numerical approach Calcolo. ,vol. 10, pp. 1- 85 ,(1973) , 10.1007/BF02576418
H. Brezis, M. Sibony, Equivalence de deux inéquations variationnelles et applications Archive for Rational Mechanics and Analysis. ,vol. 41, pp. 254- 265 ,(1971) , 10.1007/BF00250529
Ronald H. W. Hoppe, Multigrid Algorithms for Variational Inequalities SIAM Journal on Numerical Analysis. ,vol. 24, pp. 1046- 1065 ,(1987) , 10.1137/0724069