From 23ee86afcc373007b15cf3b06cc2c12771e0c195 Mon Sep 17 00:00:00 2001 From: Christophe Prud'homme Date: Mon, 6 Nov 2023 14:16:23 +0100 Subject: [PATCH] fix doc section --- .../pyfeelpptoolboxes/cfpdes.linearelasticity.adoc | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/docs/user/modules/python/pages/pyfeelpptoolboxes/cfpdes.linearelasticity.adoc b/docs/user/modules/python/pages/pyfeelpptoolboxes/cfpdes.linearelasticity.adoc index 3f1690e49..87667ede1 100644 --- a/docs/user/modules/python/pages/pyfeelpptoolboxes/cfpdes.linearelasticity.adoc +++ b/docs/user/modules/python/pages/pyfeelpptoolboxes/cfpdes.linearelasticity.adoc @@ -3,6 +3,9 @@ :feelpp: Feel++ :stem: latexmath :page-jupyter: true +:sectanchors: true +:sectnums: |,all| +:tocdepth: 3 == Introduction @@ -252,7 +255,8 @@ We consider a conformal approximation of problems by Lagrangian finite elements. We suppose that stem:[\Omega] is a polyhedron of stem:[\mathbb{R}^3] and we consider a regular and conformal family of affine meshes of stem:[\Omega] that we note stem:[\left\{\mathcal{T}_h\right\}_{h>0}]. We choose as reference finite element stem:[\left\{\widehat{K}, \widehat{P}, \widehat{Sigma}\right\}] a Lagrangian finite element of degree stem:[k \geq 1]. -Homogeneous Dirichlet problem:: +=== Homogeneous Dirichlet problem + In order to construct a stem:[V_{\mathrm{D}}]-conformal approximation space, we pose [stem] ++++ @@ -292,14 +296,16 @@ Moreover, if the problem is regularizing (i.e., if there exists a constant stem The <> results from the lemma of Céa and the interpolation theorem which we apply component by component. The estimate results from the Aubin-Nitsche lemma. ==== -Pure traction problem:: +=== Pure traction problem + For the pure traction problem, one way to eliminate the arbitrary rigid displacement at the discrete level is to: [lowerroman] . impose that the displacement at one mesh node, stem:[a_0], is zero; . choose three other mesh nodes, stem:[a_1, a_2, a_3], and three unit vectors, stem:[\tau_1, \tau_2, \tau_3], such that the set stem:[\left\{\left(a_i-a_0\right) \times \tau_i\right\}_{1 \leq i \leq 3}] forms a basis of stem:[\mathbb{R}^3]; . impose that the displacement at the node stem:[a_i] along the direction stem:[\boldsymbol{\tau}_i] is zero. -[.def#def:space] +.Pure Traction approximation space +[.def#def:space-pure-traction] **** This leads to the approximation space [stem]