Weak imposition of Dirichlet bc through Lagrange multiplier

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  1. The way I derive the equation is through the minimization of the energy of the system. For the block formulation, in principle you could define a mixed element and use it instead of the block formulation. I dislike this, and that is why I do not propose it in the tutorial. You are welcome to try, and report any issue in the multiphenicsx bug tracker.
  2. The unknown of an elasticity problem is the displacement u, while sigma in your formulation is a stress. Boundary conditions on u are Dirichlet conditions, boundary conditions on the stress are Neumann conditions. There is no need to use a Lagrange multiplier for sigma (Neumann), since that naturally becomes a boundary integral on the right-hand side.
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