From 1b1625f200e391ace869201103c040754b2855e8 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Tue, 5 May 2020 15:39:56 -0600 Subject: [PATCH] Clarify what this class actually computes. --- include/deal.II/numerics/error_estimator.h | 18 ++++++++++++++---- 1 file changed, 14 insertions(+), 4 deletions(-) diff --git a/include/deal.II/numerics/error_estimator.h b/include/deal.II/numerics/error_estimator.h index 786be94d54..dfe0c61d0e 100644 --- a/include/deal.II/numerics/error_estimator.h +++ b/include/deal.II/numerics/error_estimator.h @@ -87,11 +87,21 @@ namespace hp * \eta_K^2 * = * \sum_{F\in\partial K} - * c_F \int_{\partial K_F} \left[a \frac{\partial u_h}{\partial n}\right]^2 + * c_F \int_{\partial K_F} \jump{a \frac{\partial u_h}{\partial n}}^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 + * be the error estimator for cell $K$. $\jump{\cdot}$ denotes the jump of the + * function in square brackets at the face, and $c_F$ is a factor discussed + * below. This is the general form of the interface terms of the error + * estimator derived by Kelly et al. in the paper referenced above. The overall + * error estimate is then computed as + * @f[ + * \eta^2 = \sum_K \eta_K^2 + * @f] + * so that $\eta \approx \|\nabla (u-u_h)\|$ for the Laplace equation. The + * functions of this class compute a vector of values that corresponds to + * $\eta_K$ (i.e., the square root of the quantity above). + * + * 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 $c_F=\frac {h_F}{2p_F}$, -- 2.39.5