Abstract
We consider finite element discretizations of variational problems which correspond to quasilinear elliptic boundary value problems with linear constraints. A modified block-relaxation method and a preconditioned conjugate gradient algorithm are presented which generalize known methods for bound-constraints to more general restrictions. Global convergence proofs are given and an application to the contact problem for two membranes.
Keywords
- Contact Problem
- Finite Element Discretizations
- Convergence Proof
- Preconditioned Conjugate Gradient Method
- Descent Property
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References
Glowinski, R., Lions, J. L., Tremolieres, R., Approximations des inéquations variationelles. Paris, Dunod 1976
Kikuchi, N., Oden, J. T., Contact porblems in elasticity, TICOM report 79-8, University of Texas at Austin 1979
McCormick, G. P., Anti-zig-zagging by bending, Manag. Sci. 15, 315–320 (1969)
Mittelmann, H. D., On the approximate solution of nonlinear variational inequalities, Numer. Math. 29, 451–462 (1978)
Mittelmann, H. D., On the efficient solution of nonlinear finite element equations I, to appear in Numer. Math.
Mittelmann, H. D., On the efficient solution of nonlinear finite element equations II, submitted to Numer. Math.
Oden, J. T., Kikuchi, N., Finite element methods for certain free boundary value problems in mechanics, in "Moving boundary problems", D. G. Wilson, A. D. Solomon, P.T. Boggs (eds.), Academic Press, New York 1978
Oetli, W., Einzelschrittverfahren zur Lösung konvexer und dualkonvexer Minimierungsprobleme, Z. Angew. Math. Mech. 54, 334–351 (1974)
O'Leary, D. P., Conjugate gradient algorithms in the solution of optimization problems for nonlinear elliptic partial differential equations. Computing 22, 59–77 (1979)
Ortega, J. M., Rheinboldt, W. C., Iterative solution of nonlinear equations in several variables. Academic Press, New York 1970
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© 1981 Springer-Verlag
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Mittelmann, H.D. (1981). On the numerical solution of contact problems. In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090685
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DOI: https://doi.org/10.1007/BFb0090685
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10871-9
Online ISBN: 978-3-540-38781-7
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