Local Stability Conditions for the Babuska Method of Lagrange Multipliers
نویسنده
چکیده
We consider the so-called Babuska method of finite elements with Lagrange multipliers for numerically solving the problem Au = f in il, u = g on 3Í2, iî C Rn, 7i > 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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