From ed345d479443deb82c555dfa4a1235cae4470ef9 Mon Sep 17 00:00:00 2001 From: Marc Fehling Date: Sun, 3 May 2020 00:29:42 +0200 Subject: [PATCH] Formula for hp-refinement: Adjusted doc to what we are actually doing in the code. --- include/deal.II/hp/refinement.h | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/include/deal.II/hp/refinement.h b/include/deal.II/hp/refinement.h index 10756ba5d0..8440b66827 100644 --- a/include/deal.II/hp/refinement.h +++ b/include/deal.II/hp/refinement.h @@ -465,14 +465,13 @@ namespace hp * both meshes. * * In the context, we assume that the local error on a cell that will be - * h-refined, will lead to errors on the $2^\text{dim}$ children that are - * all equal, whereas local errors on siblings will be summed up on the - * parent cell in case of h-coarsening. This assumption is often not - * satisfied in practice: For example, if a cell is at a corner singularity, - * then the one child cell that ends up closest to the singularity will - * inherit the majority of the remaining error -- but this function can not - * know where the singularity will be, and consequently assumes equal - * distribution. + * h-refined, will be divided equally on all $n_{K_c}$ children, whereas + * local errors on siblings will be summed up on the parent cell in case of + * h-coarsening. This assumption is often not satisfied in practice: For + * example, if a cell is at a corner singularity, then the one child cell + * that ends up closest to the singularity will inherit the majority of the + * remaining error -- but this function can not know where the singularity + * will be, and consequently assumes equal distribution. * * Incorporating the transfer from the old to the adapted mesh, the complete * error prediction algorithm reads as follows: @@ -487,7 +486,7 @@ namespace hp * \gamma_\text{p}^{(p_{K,\text{future}} - p_K)}$ * $\gamma_\text{p} \in (0,1)$ * hp-refinement - * $\left( \eta_{K_c,\text{pred}} \right)^2 = 0.5^{\text{dim}} + * $\left( \eta_{K_c,\text{pred}} \right)^2 = n_{K_c}^{-1} * \left( \eta_{K_p} \, * \gamma_\text{h} \, 0.5^{p_{K_c,\text{future}}} \, * \gamma_\text{p}^{(p_{K_c,\text{future}} - p_{K_p})} \right)^2 -- 2.39.5