Abstract
The study of the finite-element method for the solution of a variety of complicated scientific problems has enjoyed a period of intense activity and stimulation, because of its simplicity in concept and elegance in development. These qualities have led eventually to its growing acceptance as a promising technique equipped with a powerful mathematical basis. The finite-element method operates on the subdomain principle; this means that the domain of the equation to be solved is usually divided into a number of separate regions or subdomains. The unknown solution function is then approximated in each subdomain by some functions, generally known as pyramid functions or basis functions.
In the present article, the Ritz penalty method, which is based on finite-element processes, is the programming method used for establishing our numerical results. Our intent is to demonstrate extensively the effect of large penalty constants on the profile of the inputU(x,t) that minimizes the diffusion control problem, Problem (P1). We show that, as the penalty constant tends to infinity in an attempt to attain close constraint satisfaction, the rate of convergence of our method deteriorates sharply.
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Communicated by G. Leitmann
This work forms part of a thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy, University of Leeds, Leeds, England.
The author acknowledges gratefully the guidance, encouragement, and keen enthusiasm of Dr. J. E. Rubio. The author also expresses his deep gratitude to Professor G. Leitmann for a number of stimulating and enlightening discussions.
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Ibiejugba, M.A. On the ritz penalty method for solving the control of a diffusion equation. J Optim Theory Appl 39, 431–449 (1983). https://doi.org/10.1007/BF00934548
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DOI: https://doi.org/10.1007/BF00934548