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Boundary Lagrange multipliers in finite element methods: Error analysis in natural norms. (English) Zbl 0765.65102
A finite element procedure for circumventing the Babuška-Brezzi condition in mixed formulations with Lagrange multipliers defined on the boundary is presented. The idea is to provide stability to the multiplier by adding residual terms constructed from the Euler-Lagrange equation to the classical Galerkin formulation while preserving consistency.
A symmetric conditionally stable method and a nonsymmetric absolutely stable one are shown to be consistent and converge in a natural mesh- independent norm. One order increase in the rate of convergence for the displacement in \(L_ 2\) is also obtained under standard assumptions on regularity.
Reviewer: V.Arnăutu (Iaşi)

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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References:
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