From 4b9530c4548b82ad436338ed2a50dd8c86fc757a Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Tue, 5 May 2020 15:34:13 -0600 Subject: [PATCH] Improve the formatting of a formula in a .h file. This doesn't change the output, just whether or not it's readable in the source file. It isn't right now :-) --- include/deal.II/numerics/error_estimator.h | 15 ++++++++++----- 1 file changed, 10 insertions(+), 5 deletions(-) diff --git a/include/deal.II/numerics/error_estimator.h b/include/deal.II/numerics/error_estimator.h index a5d9bc0291..786be94d54 100644 --- a/include/deal.II/numerics/error_estimator.h +++ b/include/deal.II/numerics/error_estimator.h @@ -82,15 +82,20 @@ namespace hp * *

Implementation

* - * In principle, the implementation of the error estimation is simple: let \f[ - * \eta_K^2 = \sum_{F\in\partial K} c_F \int_{\partial K_F} \left[a - * \frac{\partial u_h}{\partial n}\right]^2 do \f] be the error estimator for + * In principle, the implementation of the error estimation is simple: let + * @f[ + * \eta_K^2 + * = + * \sum_{F\in\partial K} + * c_F \int_{\partial K_F} \left[a \frac{\partial u_h}{\partial n}\right]^2 + * @f] + * be the error estimator for * cell $K$. $[\cdot]$ denotes the jump of the argument at the face. In the * paper of Ainsworth $ c_F=\frac {h_K}{24} $, but this factor is a bit * esoteric, stemming from interpolation estimates and stability constants which * may hold for the Poisson problem, but may not hold for more general - * situations. Alternatively, we consider the case when $ c_F=\frac {h_F}{2p_F} - * $, where $ h_F $ is face diagonal and $ p_F=max(p^+,p^-) $ is the maximum + * situations. Alternatively, we consider the case when $c_F=\frac {h_F}{2p_F}$, + * where $h_F$ is face diagonal and $p_F=max(p^+,p^-)$ is the maximum * polynomial degree of adjacent elements; or $c_F=h_K$. The choice between * these factors is done by means of the enumerator, provided as the last * argument in all functions. -- 2.39.5