On the Methods of Penalty Functions and Lagrange's Multipliers in the Abstract Neumann Problem

On approximation of the Neumann problem by the penalty method

“…Further, we will follow some ideas of [7]. The left-hand side of (2.4) obviously represents a sesquilinear Hermitian continuous form on V x V. We show now that For exact penalty methods in a finite dimensional space see also [16].…”

“…3 Remark 3.3. For further application to a linear elasticity problém we refer to [7], where the assumption (A3) is satisfied due to Koriťs inequality [6]. In [8], periodic boundary conditions in linear elasticity are treated by the proposed method based upon the assumptions (A1)-(A5).…”