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