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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.

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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


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.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1113-1129
  • MSC: Primary 65N30
  • DOI:
  • MathSciNet review: 583490