// cell->is_artificial()</code> is true. The simplest way, however, is to
// simply ask the cell whether it is owned by the local processor.
// - Copying local contributions into the global matrix must include
- // distributing constraints and boundary values. In other words, we can now
+ // distributing constraints and boundary values. In other words, we cannot
// (as we did in step-6) first copy every local contribution into the global
// matrix and only in a later step take care of hanging node constraints and
// boundary values. The reason is, as discussed in step-17, that PETSc does
// not provide access to arbitrary elements of the matrix once they have
- // been assembled into it -- in parts because they may simple no longer
+ // been assembled into it -- in parts because they may simply no longer
// reside on the current processor but have instead been shipped to a
// different machine.
// - The way we compute the right hand side (given the