Abstract
We prove the convergence and estimate the error of a general algorithm for the minimization of non-quadratic functionals over a convex set in a reflexive Banach space, provided that the convex set verifies a certain assumption. In the case of the Sobolev spaces, our algorithm is exactly a variant of the Schwarz domain decomposition method, and we prove that the introduced assumption holds if the convex set is defined by constraints on the function values almost everywhere in the domain. In the end of the paper we give some numerical examples concerning the two-obstacle problem of a nonlinear elastic membrane.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35690-7_44
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Badea, L. (2003). Convergence Rate of a Multiplicative Schwarz Method for Strongly Nonlinear Variational Inequalities. In: Barbu, V., Lasiecka, I., Tiba, D., Varsan, C. (eds) Analysis and Optimization of Differential Systems. SEC 2002. IFIP — The International Federation for Information Processing, vol 121. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35690-7_4
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DOI: https://doi.org/10.1007/978-0-387-35690-7_4
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