From 5ead9bd20f0a5d857ac1e90c4bd94b1c2c528845 Mon Sep 17 00:00:00 2001 From: heister Date: Wed, 31 Jul 2013 01:33:58 +0000 Subject: [PATCH] documentation patch by Oleh Krehel git-svn-id: https://svn.dealii.org/trunk@30187 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-13/step-13.cc | 4 ++-- deal.II/examples/step-14/step-14.cc | 6 +++--- deal.II/examples/step-15/doc/intro.dox | 4 ++-- deal.II/examples/step-36/doc/intro.dox | 2 +- 4 files changed, 8 insertions(+), 8 deletions(-) diff --git a/deal.II/examples/step-13/step-13.cc b/deal.II/examples/step-13/step-13.cc index b467f58c9b..df0d8d2342 100644 --- a/deal.II/examples/step-13/step-13.cc +++ b/deal.II/examples/step-13/step-13.cc @@ -848,8 +848,8 @@ namespace Step13 // 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 - // return, we also have to unlock the mutex. This all - // is not be a problem here, but we want to show the general + // return, 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 diff --git a/deal.II/examples/step-14/step-14.cc b/deal.II/examples/step-14/step-14.cc index 27a3b6c3da..f91bbfc666 100644 --- a/deal.II/examples/step-14/step-14.cc +++ b/deal.II/examples/step-14/step-14.cc @@ -2589,7 +2589,7 @@ namespace Step14 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 home-manythe + // neighboring cell we have to work, i.e. the how-many'th 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 neighbor_neighbor: @@ -2671,7 +2671,7 @@ namespace Step14 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 @@ -2836,7 +2836,7 @@ namespace Step14 // 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; diff --git a/deal.II/examples/step-15/doc/intro.dox b/deal.II/examples/step-15/doc/intro.dox index 33494379eb..344cd54f5f 100644 --- a/deal.II/examples/step-15/doc/intro.dox +++ b/deal.II/examples/step-15/doc/intro.dox @@ -95,7 +95,7 @@ u^{0}=g$ in the first step and with $\delta u^{n}=0$ in all the following steps.

Weak formulation of the problem

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 @@ -112,7 +112,7 @@ Reducing this space to a finite dimensional space with basis $\left\{ \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[ diff --git a/deal.II/examples/step-36/doc/intro.dox b/deal.II/examples/step-36/doc/intro.dox index 69a89c4574..48d23ae0fd 100644 --- a/deal.II/examples/step-36/doc/intro.dox +++ b/deal.II/examples/step-36/doc/intro.dox @@ -72,7 +72,7 @@ eigenvalue. 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 $\Psi(\mathbf x)\approx\Psi_h(\mathbf x)=\sum_{j}\phi_j(\mathbf x)\tilde\psi_j$, -- 2.39.5