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Fix oseen
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Signed-off-by: Umberto Zerbinati <[email protected]>
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Umberto Zerbinati committed Jun 7, 2024
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Expand Up @@ -2,6 +2,7 @@ Vertex Patch smoothing for Augmented Lagrangian formulations of the Oseen proble
===================================================================================

In this tutorial, we will see how to use an augmented Lagrangian formulation to precondition the Oseen problem, i.e.

.. math::
\text{Given }\vec{\beta}\in \mathbb{R}^3 \text{ find } (\vec{u},p) \in [H^1_{0}(\Omega)]^d\times L^2(\Omega) \text{ s.t. }
Expand All @@ -10,6 +11,7 @@ In this tutorial, we will see how to use an augmented Lagrangian formulation to
\nu (\nabla \vec{u},\nabla \vec{v})_{L^2(\Omega)} + (\nabla\cdot \vec{v}, p)_{L^2(\Omega)} -(\nabla \vec{u}\vec{\beta},\vec{v})_{L^2(\Omega)} + (div(\vec{u}),div(\vec{v}))_{L^2(\Omega)} = (\vec{f},\vec{v})_{L^2(\Omega)} \qquad \forall v\in H^1_{0}(\Omega)\\
(\nabla\cdot \vec{u},q)_{L^2(\Omega)} = 0 \qquad \froall q\in L^2(\Omega)
\end{cases}
Let us begin defining the parameters of the problem. ::

from ngsolve import *
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