Ladyzhenskaya–Babuška–Brezzi condition
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In numerical partial differential equations, the Ladyzhenskaya–Babuška–Brezzi (LBB) condition is a sufficient condition for a saddle point problem to have a unique solution that depends continuously on the input data. Saddle point problems arise in the discretization of Stokes flow and in the mixed finite element discretization of Poisson's equation. For positive-definite problems, like the unmixed formulation of the Poisson equation, most discretization schemes will converge to the true solution in the limit as the mesh is refined. For saddle point problems, however, many discretizations are unstable, giving rise to artifacts such as spurious oscillations. The LBB condition gives criteria for when a discretization of a saddle point problem is stable.
The condition is variously referred to as the LBB condition, the Babuška–Brezzi condition, or the "inf-sup" condition.