// Our next task is to define the right hand side of our problem (i.e., the
// scalar right hand side for the pressure in the original Laplace
- // equation), boundary values for the pressure, as well as a function that
+ // equation), boundary values for the pressure, and a function that
// describes both the pressure and the velocity of the exact solution for
// later computations of the error. Note that these functions have one, one,
// and <code>dim+1</code> components, respectively, and that we pass the
// And then we also have to define these respective functions, of
// course. Given our discussion in the introduction of how the solution
- // should look like, the following computations should be straightforward:
+ // should look, the following computations should be straightforward:
template <int dim>
double RightHandSide<dim>::value(const Point<dim> & /*p*/,
const unsigned int /*component*/) const
// real-life porous media flow simulations, and we would like to use the
// opportunity to demonstrate the technique to use tensor valued functions.
//
- // Possibly unsurprising, deal.II also has a base class not only for scalar
+ // Possibly unsurprisingly, deal.II also has a base class not only for scalar
// and generally vector-valued functions (the <code>Function</code> base
// class) but also for functions that return tensors of fixed dimension and
// rank, the <code>TensorFunction</code> template. Here, the function under
std::vector<Tensor<2, dim>> & values) const
{
// The value we are going to store for a given point does not depend on its
- // coordinates and we use the `points` object only for checking that the
+ // coordinates, and we use the `points` object only for checking that the
// `values` object has the correct size. In release mode, `AssertDimension`
- // is defined empty and the compiler will complain that the `points` object
+ // is defined empty, and the compiler will complain that the `points` object
// is unused. The following line silences this warning.
(void)points;
AssertDimension(points.size(), values.size());
// velocities and pressures are not intermingled: First all velocity
// degrees of freedom, then all pressure DoFs. This way, the global matrix
// separates nicely into a $2 \times 2$ system. To achieve this, we have to
- // renumber degrees of freedom base on their vector component, an
+ // renumber degrees of freedom based on their vector component, an
// operation that conveniently is already implemented:
DoFRenumbering::component_wise(dof_handler);