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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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