diff --git a/docs/src/PETScPC/oseen.py.rst b/docs/src/PETScPC/oseen.py.rst index 5ed0637..c04893e 100755 --- a/docs/src/PETScPC/oseen.py.rst +++ b/docs/src/PETScPC/oseen.py.rst @@ -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} diff --git a/docs/src/PETScPC/stokes.py.rst b/docs/src/PETScPC/stokes.py.rst index fba4dce..9de24dd 100755 --- a/docs/src/PETScPC/stokes.py.rst +++ b/docs/src/PETScPC/stokes.py.rst @@ -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: :: diff --git a/docs/src/PETScSNES/hyperelasticity.py.rst b/docs/src/PETScSNES/hyperelasticity.py.rst index 6746732..51c4516 100644 --- a/docs/src/PETScSNES/hyperelasticity.py.rst +++ b/docs/src/PETScSNES/hyperelasticity.py.rst @@ -89,4 +89,3 @@ We compare the performance of the two solvers, in the following table: - 10 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. -""" \ No newline at end of file