Local stability conditions for the Babuška method of Lagrange multipliers

Author:
Juhani Pitkäranta

Journal:
Math. Comp. **35** (1980), 1113-1129

MSC:
Primary 65N30

MathSciNet review:
583490

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Abstract: We consider the so-called Babuška method of finite elements with Lagrange multipliers for numerically solving the problem in , on , , . 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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DOI:
https://doi.org/10.1090/S0025-5718-1980-0583490-9

Article copyright:
© Copyright 1980
American Mathematical Society