Static condensation
=====================

Field :math:`\delta` disappears from the overall formulation thanks to static condensation. At each collocation point :math:`{s}_{g}`, we have (according to eq.1.4):

:math:`{t}_{g}\mathrm{=}{\lambda }_{g}+r({g}_{g}\mathrm{-}{\delta }_{g})\mathrm{\in }\mathrm{\partial }\Pi ({\delta }_{g})`

with :math:`{t}_{g}\mathrm{=}t({s}_{g})`, :math:`{\lambda }_{g}\mathrm{=}\lambda ({s}_{g})`, :math:`{g}_{g}\mathrm{=}g({s}_{g})`, and :math:`{\delta }_{g}\mathrm{=}\delta ({s}_{g})`.

Once the problem is discretized, :math:`{g}_{g}` and :math:`{\lambda }_{g}` will be obtained by interpolations with the appropriate form functions of the discretized values at the nodes of :math:`g` and :math:`\lambda` that are denoted by :math:`\mathrm{\{}G\mathrm{\}}` and :math:`\{\Lambda \}`.

The integration of the constitutive relationship (see below) makes it possible to calculate :math:`{\delta }_{g}` as a function of :math:`\mathrm{\{}G\mathrm{\}}` and :math:`\mathrm{\{}\Lambda \mathrm{\}}`, which is denoted by :math:`\delta`:

:math:`{t}_{g}\mathrm{=}{\lambda }_{g}+r({g}_{g}\mathrm{-}{\delta }_{g})\mathrm{\in }\mathrm{\partial }\Pi ({\delta }_{g})\mathrm{\iff }{\delta }_{g}\mathrm{=}\stackrel{ˆ}{\delta }({g}_{g},{\lambda }_{g})\mathrm{=}\delta (\mathrm{\{}G\mathrm{\}},\mathrm{\{}\Lambda \mathrm{\}})`