Analysis and approximation of optimal control problems for a simplified Ginzburg-Landau model of superconductivity |
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| Authors: | Max D. Gunzburger L. Steven Hou S.S. Ravindran |
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| Affiliation: | (1) Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0531, USA , US;(2) Department of Mathematics and Statistics, York University, North York, Ontario M3J 1P3, Canada , CA;(3) Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27606-8205, USA , US |
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| Abstract: | Summary. This paper is concerned with optimal control problems for a Ginzburg-Landau model of superconductivity that is valid for high values of the Ginzburg-Landau parameter and high external fields. The control is of Neumann type. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Then we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations. Finally, we report on some numerical results. Received May 3, 1994 / Revised version received November 28, 1995 |
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| Keywords: | Mathematics Subject Classification (1991): 65N30 49J20 35J65 81Q05 |
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