From d1ba8b64981932a6fab3d6b6d5d9a2e08c99d20b Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Mon, 19 Sep 2016 21:04:25 -0600 Subject: [PATCH] Drop the name 'Fichera corner', plus other updates. --- include/deal.II/grid/grid_generator.h | 32 +++++++++++++++++++-------- 1 file changed, 23 insertions(+), 9 deletions(-) diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h index 72bf924b1b..267d57e8ba 100644 --- a/include/deal.II/grid/grid_generator.h +++ b/include/deal.II/grid/grid_generator.h @@ -598,18 +598,32 @@ namespace GridGenerator /** * Initialize the given triangulation with a hyper-L (in 2d or 3d) - * consisting of exactly 2^dim-1 cells. It produces the hypercube - * with the interval [left,right] without the hypercube made out of - * the interval [(left+right)/2,right] for each coordinate. If the - * @p colorize flag is set, the @p boundary_ids of the surfaces are - * assigned, such that the left boundary is 0, and the others are set with - * growing number accordingly to the counterclockwise. Colorize option works - * only with 2-dimensional problem. This function will create the classical - * L-shape in 2d and it will look like the following in 3d: + * consisting of exactly 2^dim-1 cells. It produces the + * hypercube with the interval [left,right] without the + * hypercube made out of the interval [(left+right)/2,right] + * for each coordinate. Because the domain is about the simplest one + * with a reentrant (i.e., non-convex) corner, solutions of many + * partial differential equation have singularities at this + * corner. That is, at the corner, the gradient or a higher + * derivative (depending on the boundary conditions chosen) does not + * remain bounded. As a consequence, this domain is often used to + * test convergence of schemes when the solution lacks regularity. + * + * If the @p colorize flag is set, the @p boundary_ids of the + * surfaces are assigned, such that the left boundary is 0, and the + * others are set with growing number accordingly to the + * counterclockwise. Colorize option works only with 2-dimensional + * problem. This function will create the classical L-shape in 2d + * and it will look like the following in 3d: * * @image html hyper_l.png * - * This function is declared to exist for triangulations of all space + * @note The 3d domain is also often referred to as the "Fichera corner", + * named after Gaetano Fichera (1922-1996) who first computed an + * approximation of the corner singularity exponent of the lowest + * eigenfunction of the domain. + * + * This function exists for triangulations of all space * dimensions, but throws an error if called in 1d. * * @note The triangulation needs to be void upon calling this function. -- 2.39.5