// lead to deadlocks. A similar situation arises, when one changes
// the code to have a return statement somewhere in the middle of
// the locked block, and forgets that before we call
- // <code>return</code>, we also have to unlock the mutex. This all
- // is not be a problem here, but we want to show the general
+ // <code>return</code>, we also have to unlock the mutex. All this
+ // is no problem here, but we want to show the general
// technique to cope with these problems nevertheless: have an
// object that upon initialization (i.e. in its constructor) locks
// the mutex, and on running the destructor unlocks it again. This
Assert (cell->neighbor(face_no).state() == IteratorState::valid,
ExcInternalError());
// If we have that, then we need to find out with which face of the
- // neighboring cell we have to work, i.e. the <code>home-many</code>the
+ // neighboring cell we have to work, i.e. the <code>how-many'th</code> the
// neighbor the present cell is of the cell behind the present face. For
// this, there is a function, and we put the result into a variable with
// the name <code>neighbor_neighbor</code>:
ExcInternalError());
// Then find out which neighbor the present cell is of the adjacent
- // cell. Note that we will operator on the children of this adjacent
+ // cell. Note that we will operate on the children of this adjacent
// cell, but that their orientation is the same as that of their mother,
// i.e. the neigbor direction is the same.
const unsigned int
// Finally, we have a variable that denotes the maximum number of
// degrees of freedom we allow for the (primal) discretization. If it is
- // exceeded, we stop the process of solving and intermittend mesh
+ // exceeded, we stop the process of solving and intermittent mesh
// refinement. Its default value is 20,000.
unsigned int max_degrees_of_freedom;
<h3>Weak formulation of the problem</h3>
Starting with the strong formulation above, we get the weak formulation by multiplying
-both sides of the PDE with a testfunction $\varphi$ and integrating by parts on both sides:
+both sides of the PDE with a test function $\varphi$ and integrating by parts on both sides:
@f[
\left( \nabla \varphi , \frac{1}{(1+|\nabla u^{n}|^{2})^{\frac{1}{2}}}\nabla
\delta u^{n} \right)-\left(\nabla \varphi ,\frac{\nabla u^{n} \cdot \nabla
\delta u^{n}=\sum_{j=0}^{N-1} U_{j} \varphi_{j}
@f]
-Using the basis functions as testfunctions and defining $a_{n}:=\frac{1}
+Using the basis functions as test functions and defining $a_{n}:=\frac{1}
{\sqrt{1+|\nabla u^{n}|^{2}}}$, we can rewrite the weak formualtion:
@f[
In order to numerically find solutions to this equation, i.e. a set of
pairs of eigenvalues/eigenfunctions, we use the usual finite element
-approach of multiplying the equation from the left with testfunctions,
+approach of multiplying the equation from the left with test functions,
integrating by parts, and searching for solutions in finite
dimensional spaces by approximating $\Psi(\mathbf
x)\approx\Psi_h(\mathbf x)=\sum_{j}\phi_j(\mathbf x)\tilde\psi_j$,
projects / dealii-svn.git / commitdiff