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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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4 changes: 2 additions & 2 deletions docs/src/PETScPC/oseen.py.rst
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Expand Up @@ -3,8 +3,8 @@ 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::
.. 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. }
\begin{cases}
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2 changes: 1 addition & 1 deletion docs/src/PETScPC/stokes.py.rst
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Expand Up @@ -10,7 +10,7 @@ In particular, we will consider a Bernardi-Raugel inf-sup stable discretization
\begin{cases}
(\nabla \vec{u},\nabla \vec{v})_{L^2(\Omega)} + (\nabla\cdot \vec{v}, p)_{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)
(\nabla\cdot \vec{u},q)_{L^2(\Omega)} = 0 \qquad \forall q\in L^2(\Omega)
\end{cases}
Such a discretization can easily be constructed using NGSolve as follows: ::
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1 change: 0 additions & 1 deletion docs/src/PETScSNES/hyperelasticity.py.rst
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Expand Up @@ -89,4 +89,3 @@ We compare the performance of the two solvers, in the following table:
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This suggests that while NGS non-linear solver when finely tuned performs as well as PETSc SNES, it is more sensitive to the choice of the damping factor. In this case, a damping factor of 0.3 was found to be the best choice.
"""

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