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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Sharp error estimates for a finite element-penalty approach to a class of regulator problems
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by Goong Chen, Wendell H. Mills, Shun Hua Sun and David A. Yost PDF
Math. Comp. 40 (1983), 151-173 Request permission


Quadratic cost optimal controls can be solved by penalizing the governing linear differential equation [2], [9]. In this paper, we study the numerical analysis of this approach using finite elements. We formulate the geometric condition (H) which requires that pairs of certain related finite-dimensional approximation spaces form “angles” which are bounded away from the “$180^\circ$ angle”. Under condition (H), we prove that the penalty parameter $\varepsilon$ and the discretization parameter h are independent in the error bounds, thereby giving sharp asymptotic error estimates. This condition (H) is shown to be also a necessary condition for such independence. Examples and numerical evidence are also provided.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 151-173
  • MSC: Primary 65K10; Secondary 49D30
  • DOI:
  • MathSciNet review: 679438