Integral Identity and Estimate of the Deviation of Approximate Solutions of a Biharmonic Obstacle Problem

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Resumo

We show that the integral identity obtained by D.E. Apushkinskaya and S.I. Repin (2020) for approximate solutions of the biharmonic obstacle problem that satisfy a pointwise constraint on the second divergence is valid for arbitrary approximate solutions. Using this result, we obtain a new estimate for the deviation of approximate solutions from exact ones in the case when the approximate solutions do not satisfy the pointwise constraint on the second divergence.

Sobre autores

K. Besov

Steklov Mathematical Institute of Russian Academy of Sciences; Institute of Mathematics and Mathematical Modeling

Autor responsável pela correspondência
Email: kbesov@mi-ras.ru
119991, Moscow, Russia; 050010, Almaty, Kazakhstan

Bibliografia

  1. Апушкинская Д.Е., Репин С.И. Бигармоническая задача с препятствием: гарантированные и вычисляемые оценки ошибок для приближенных решений // Ж. вычисл. матем. и матем. физ. 2020. Т. 60. № 11. С. 1881–1897.
  2. Caffarelli L.A., Friedman A. The obstacle problem for the biharmonic operator // Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 1979. V. 6. P. 151–184.
  3. Frehse J. On the regularity of the solution of the biharmonic variational inequality // Manuscr. Math. 1973. V. 9. P. 91–103.
  4. Стейн И.М. Сингулярные интегралы и дифференциальные свойства функций. М.: Мир, 1973.
  5. Scherfgen D. Integral calculator. https://www.integral-calculator.com.

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