NUMERICAL APPROXIMATION OF A ONE-DIMENSIONAL ELLIPTIC OPTIMAL DESIGN PROBLEM

Casado-Diaz J, Castro C, Luna-Laynez M, Zuazua E (2011)

Publication Type: Journal article

Publication year: 2011

Journal

Multiscale Modeling & Simulation Society for Industrial and Applied Mathematics

Book Volume: 9

Pages Range: 1181-1216

Journal Issue: 3

DOI: 10.1137/10081928X

Abstract

We address the numerical approximation by finite-element methods of an optimal design problem for a two phase material in one space dimension. This problem, in the continuous setting, due to high frequency oscillations, often does not have a classical solution, and a relaxed formulation is needed to ensure existence. On the contrary, the discrete versions obtained by numerical approximation have a solution. In this article we prove the convergence of the discretizations and obtain convergence rates. We also show a faster convergence when the relaxed version of the continuous problem is taken into account when building the discretization strategy. In particular it is worth emphasizing that, even when the original problem has a classical solution so that relaxation is not necessary, numerical algorithms converge faster when implemented on the relaxed version.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Seville / Universidad de Sevilla ES Spain (ES) Universidad Politécnica de Madrid (UPM) ES Spain (ES) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Casado-Diaz, J., Castro, C., Luna-Laynez, M., & Zuazua, E. (2011). NUMERICAL APPROXIMATION OF A ONE-DIMENSIONAL ELLIPTIC OPTIMAL DESIGN PROBLEM. Multiscale Modeling & Simulation, 9(3), 1181-1216. https://dx.doi.org/10.1137/10081928X

MLA:

Casado-Diaz, Juan, et al. "NUMERICAL APPROXIMATION OF A ONE-DIMENSIONAL ELLIPTIC OPTIMAL DESIGN PROBLEM." Multiscale Modeling & Simulation 9.3 (2011): 1181-1216.

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