From: Wolfgang Bangerth Date: Tue, 20 Nov 2018 04:02:01 +0000 (-0700) Subject: Better format a couple of formulas in step-46. X-Git-Tag: v9.1.0-rc1~550^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F7455%2Fhead;p=dealii.git Better format a couple of formulas in step-46. --- diff --git a/examples/step-46/doc/intro.dox b/examples/step-46/doc/intro.dox index 57b3ccd6a1..77305ac75a 100644 --- a/examples/step-46/doc/intro.dox +++ b/examples/step-46/doc/intro.dox @@ -78,19 +78,21 @@ multiplying from the left by a test function and integrating over the domain. It then looks like this: Find $y = \{\mathbf v, p, \mathbf u\} \in Y \subset H^1(\Omega_f)^d \times L_2(\Omega_f) \times H^1(\Omega_s)^d$ such that -@f{multline*} +@f{align*} 2 \eta (\varepsilon(\mathbf a), \varepsilon(\mathbf v))_{\Omega_f} - (\nabla \cdot \mathbf a, p)_{\Omega_f} - - (q, \nabla \cdot \mathbf v)_{\Omega_f} + - (q, \nabla \cdot \mathbf v)_{\Omega_f} & \\ - + (\varepsilon(\mathbf b), C \varepsilon(\mathbf u))_{\Omega_s} + + (\varepsilon(\mathbf b), C \varepsilon(\mathbf u))_{\Omega_s} & \\ - (\mathbf b, (2 \eta \varepsilon(\mathbf v) + p \mathbf 1) \mathbf n)_{\Gamma_i} - = + &= 0, @f} -for all test functions $\mathbf a, q, \mathbf b$. +for all test functions $\mathbf a, q, \mathbf b$; the first, second, and +third lines correspond to the fluid, solid, and interface +contributions, respectively. Note that $Y$ is only a subspace of the spaces listed above to accommodate for the various Dirichlet boundary conditions. @@ -298,16 +300,16 @@ points: Let us first discuss implementing the bilinear form, which at the discrete level we recall to be -@f{multline*} +@f{align*} 2 \eta (\varepsilon(\mathbf a_h), \varepsilon(\mathbf v_h))_{\Omega_f} - (\nabla \cdot \mathbf a_h, p_h)_{\Omega_f} - - (q_h, \nabla \cdot \mathbf v_h)_{\Omega_f} + - (q_h, \nabla \cdot \mathbf v_h)_{\Omega_f} & \\ - + (\varepsilon(\mathbf b_h), C \varepsilon(\mathbf u_h))_{\Omega_s} + + (\varepsilon(\mathbf b_h), C \varepsilon(\mathbf u_h))_{\Omega_s} & \\ - (\mathbf b_h, (2 \eta \varepsilon(\mathbf v_h) + p \mathbf 1) \mathbf n)_{\Gamma_i} - = + &= 0, @f} Given that we have extended the fields by zero, we could in principle