From 50eae5b525fee6df7142083e6cd256e92ae892c5 Mon Sep 17 00:00:00 2001 From: Marc Fehling Date: Thu, 28 May 2020 20:02:48 +0200 Subject: [PATCH] Added additional sentence describing the hp-interface. Format code in listing. --- 9.2/paper.tex | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/9.2/paper.tex b/9.2/paper.tex index bdcb88d..c61ab85 100644 --- a/9.2/paper.tex +++ b/9.2/paper.tex @@ -519,20 +519,22 @@ Consider the following (incomplete) listing as an example: We estimate both erro smoothness of the finite element approximation. Further, we flag certain fractions of cells with the highest and lowest errors for refinement and coarsening, respectively (here: 30\%/3\%). From those cells listed for adaptation, we designate a subset -for $h$- and $p$-adaptation (here: 10\%/90\%). +for $h$- and $p$-adaptation (here: 10\%/90\%). The parameters of the corresponding +\texttt{hp::Refinement} function specify the fraction of cells to be $p$-adapted from +those subsets flagged for refinement and coarsening, respectively. \begin{c++} -Vector estimated_error_per_cell (n_active_cells); +Vector estimated_error_per_cell(n_active_cells); KellyErrorEstimator::estimate( dof_handler, ..., solution, estimated_error_per_cell, ...); GridRefinement::refine_and_coarsen_fixed_number( triangulation, estimated_error_per_cell, 0.3, 0.03); -Vector estimated_smoothness_per_cell (n_active_cells); +Vector estimated_smoothness_per_cell(n_active_cells); SmoothnessEstimator::Legendre::coefficient_decay( ..., dof_handler, solution, estimated_smoothness_per_cell); hp::Refinement::p_adaptivity_fixed_number( dof_handler, estimated_smoothness_per_cell, 0.9, 0.9); -hp::Refinement::choose_p_over_h (dof_handler); +hp::Refinement::choose_p_over_h(dof_handler); triangulation.execute_coarsening_and_refinement(); \end{c++} @@ -542,8 +544,7 @@ smoothness estimation, and made sure that they work for refinement as well as coarsening in terms of $h$- and $p$-adaptation in serial and parallel applications. The former relies on knowing an estimate for the upper error bound \cite[Thm.~3.4]{BabuskaSuri1990}. -For successive refinements, we can predict how the error will change -based on +For successive refinements, we can predict how the error will change based on current error estimates and adaptation flags. In the next refinement cycle, these predicted error estimates allow us to decide whether the choice of adaptation in the previous cycle was justified, and provide a criterion for the choice in the next -- 2.39.5