The finite element method with Lagrange multiplier on the boundary: circumventing the Babuscka-Brezzi condition

In order to circumvent the Babuska-Brezzi condition in the finite element method with Lagrange multipliers on the boundary, least-squares-like terms are added to the classical Galerkin method. The additional terms involve integrals over element interiors and mesh-parameter dependent coefficients. The resulting formulations retain consistency and attain convergence for arbitrary polynomial interpolations which are continuous for the primal variable and which may be continuous or discontinuous for the Lagrange multiplier.

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