Fixing section titles

docs/src/PETScPC/poisson.py.rst

@@ -1,5 +1,5 @@
-Preconditioning the Poisson problem
-=====================================
+Vertex Patch smoothing for p-Multigrid preconditioners
+========================================================
 
 In this tutorial, we explore using `PETSc PC` as a preconditioner inside NGSolve preconditioning infrastructure.
 We will focus our attention on the Poisson problem, and we will consider different preconditioning strategies.

docs/src/PETScPC/stokes.py.rst

@@ -1,5 +1,5 @@
-Preconditioning the Stokes problem 
-===================================
+Boffi-Lovadina Augmentation for Bernardi-Raugel discretization of the Stokes problem
+======================================================================================
 
 In this tutorial, we explore constructing preconditioners for saddle point problems using `PETSc PC`.
 In particular, we will consider a Bernardi-Raugel inf-sup stable discretization of the Stokes problem, i.e.
@@ -33,8 +33,8 @@ Such a discretization can easily be constructed using NGSolve as follows: ::
    else:
       mesh = Mesh(ngm.Mesh.Receive(COMM_WORLD))
    nu = Parameter(1.0)
-   V = VectorH1(mesh, order=4, dirichlet="wall|inlet|cyl", autoupdate=True)
-   Q = L2(mesh, order=2, autoupdate=True)
+   V = VectorH1(mesh, order=2, dirichlet="wall|inlet|cyl", autoupdate=True)
+   Q = L2(mesh, order=0, autoupdate=True)
    u,v = V.TnT(); p,q = Q.TnT()
    a = BilinearForm(nu*InnerProduct(Grad(u),Grad(v))*dx)
    a.Assemble()
@@ -184,7 +184,7 @@ This formulation can easily be constructed by adding a new velocity block in the
    gfu.Set(uin, definedon=mesh.Boundaries("inlet"))
    sol = BlockVector( [gfu.vec, gfp.vec] )
 
-   print("-----------|Augmented LU|-----------")
+   print("-----------|Boffi--Lovadina Augmentation LU|-----------")
    solvers.MinRes (mat=K, pre=C, rhs=rhs, sol=sol, tol=1e-10,
                    printrates=True, initialize=False)
    Draw(gfu)
@@ -216,7 +216,7 @@ This is not ideal for large problems, and we can use a `Hypre` preconditioner fo
    C = BlockMatrix( [ [twolvpre, None], [None, mGpre] ] )
    gfu.vec.data[:] = 0; gfp.vec.data[:] = 0;
    gfu.Set(uin, definedon=mesh.Boundaries("inlet"))
-   print("-----------|Augmented Two Level Additive Schwarz|-----------")
+   print("-----------|Boffi--Lovadina Augmentation Two Level Additive Schwarz|-----------")
    solvers.MinRes (mat=K, pre=C, rhs=rhs, sol=sol, tol=1e-10,
                    printrates=True, initialize=False)
    Draw(gfu)
@@ -345,4 +345,3 @@ We see that a purely algebraic approach based on the Sherman-Morrisson-Woodbory
      - 100 (1.06e-03)
    * - Augmentation Schermon-Morrisson-Woodbory
      - 84 (1.16e-07)
-