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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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Local stability conditions for the Babuška method of Lagrange multipliers
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by Juhani Pitkäranta PDF
Math. Comp. 35 (1980), 1113-1129 Request permission

Abstract:

We consider the so-called Babuška method of finite elements with Lagrange multipliers for numerically solving the problem $\Delta u = f$ in $\Omega$, $u = g$ on $\partial \Omega$, $\Omega \subset {R^n}$, $n \geqslant 2$. We state a number of local conditions from which we prove the uniform stability of the Lagrange multiplier method in terms of a weighted, mesh-dependent norm. The stability conditions given weaken the conditions known so far and allow mesh refinements on the boundary. As an application, we introduce a class of finite element schemes, for which the stability conditions are satisfied, and we show that the convergence rate of these schemes is of optimal order.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1113-1129
  • MSC: Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583490-9
  • MathSciNet review: 583490