From d9523905fa239980ae7a2f2f260f786cad86a42d Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Mon, 6 Mar 2006 15:31:06 +0000 Subject: [PATCH] Update docs. git-svn-id: https://svn.dealii.org/trunk@12541 0785d39b-7218-0410-832d-ea1e28bc413d --- .../numerics/derivative_approximation.h | 30 ++++++++++++------- 1 file changed, 19 insertions(+), 11 deletions(-) diff --git a/deal.II/deal.II/include/numerics/derivative_approximation.h b/deal.II/deal.II/include/numerics/derivative_approximation.h index 8057d719af..291db5f75f 100644 --- a/deal.II/deal.II/include/numerics/derivative_approximation.h +++ b/deal.II/deal.II/include/numerics/derivative_approximation.h @@ -68,20 +68,28 @@ namespace hp * each element by the correct power of the respective cell size. * * The computation of this quantity must fail if a cell has only - * neighbors for which the direction vectors do not span the whole - * space. As can easily be verified, this can only happen on very + * neighbors for which the direction vectors $y_K$ do not span the + * whole space, since then the matrix $Y$ is no longer invertible. If + * this happens, you will get an error similar to this one: + * @code + * -------------------------------------------------------- + * An error occurred in line <749> of file in function + * static void DerivativeApproximation::approximate(const Mapping&, const DH&, const InputVector&, unsigned int, const + * std::pair&, Vector&) [with DerivativeDescription = DerivativeApproximation::Gradient<3>, int + * dim = 3, DH = DoFHandler, InputVector = Vector] + * The violated condition was: + * determinant(Y) != 0 + * The name and call sequence of the exception was: + * ExcInsufficientDirections() + * Additional Information: + * (none) + * -------------------------------------------------------- + * @endcode + * As can easily be verified, this can only happen on very * coarse grids, when some cells and all their neighbors have not been * refined even once. You should therefore only call the functions of * this class if all cells are at least once refined. In practice this - * is not much of a restriction. If for some cells, the neighbors do - * not span the whole space, an exception is thrown. - * - * Note that for the computation of the quantities of this class, only - * the values of the finite element field at the centers of the cells - * are taken. It might therefore only be useful to use this class for - * discontinuous, piecewise constant elements (i.e. using the - * FEDG_Q0 class), since all other finite elements can approximate - * gradients themselves. + * is not much of a restriction. * * *

Approximation of higher derivatives

-- 2.39.5