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[Getfem-commits] (no subject)
From: |
Tetsuo Koyama |
Subject: |
[Getfem-commits] (no subject) |
Date: |
Sat, 30 Nov 2019 23:18:06 -0500 (EST) |
branch: devel-tetsuo-fix-math
commit bb0fc830115ca1f824938cdfeb9e80290553d76c
Author: Tetsuo Koyama <address@hidden>
Date: Sun Dec 1 01:58:53 2019 +0000
:bug: Integral variable
---
doc/sphinx/source/tutorial/thermo_coupling.rst | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/doc/sphinx/source/tutorial/thermo_coupling.rst
b/doc/sphinx/source/tutorial/thermo_coupling.rst
index 72ab759..8267ec1 100644
--- a/doc/sphinx/source/tutorial/thermo_coupling.rst
+++ b/doc/sphinx/source/tutorial/thermo_coupling.rst
@@ -100,9 +100,9 @@ Weak formulation of each partial differential equation is
obtained by multiplyin
.. math::
&\mbox{Find } \theta, V, u \mbox{ with } V = 0.1, u = 0 \mbox{ on the left
face}, V = 0 \mbox{ on the right face}, \\
- &\ds \int_{\Omega} \varepsilon\kappa\nabla\theta\cdot\nabla\delta_{\theta} +
2D\theta\delta_{\theta}dx = \int_{\Omega} (2DT_0 + \varepsilon\sigma|\nabla
V|^2)\delta_{\theta} dx ~~~\mbox{ for all } \delta_{\theta}, \\
- &\ds \int_{\Omega} \varepsilon\sigma\nabla V\cdot\nabla\delta_V = 0 dx ~~~
\mbox{ for all } \delta_V \mbox{ satisfying } \delta_V = 0 \mbox{ on the left
and right faces}, \\
- &\ds \int_{\Omega} \bar{\sigma}(u):\bar{\varepsilon}(\delta_u)dx =
\int_{\Gamma_N} F\cdot \delta_u d\Gamma ~~~ \mbox{ for all } \delta_{u} \mbox{
satisfying } \delta_u = 0 \mbox{ on the left face},
+ &\ds \int_{\Omega} \varepsilon\kappa\nabla\theta\cdot\nabla\delta_{\theta} +
2D\theta\delta_{\theta}d\Omega = \int_{\Omega} (2DT_0 +
\varepsilon\sigma|\nabla V|^2)\delta_{\theta} d\Omega ~~~\mbox{ for all }
\delta_{\theta}, \\
+ &\ds \int_{\Omega} \varepsilon\sigma\nabla V\cdot\nabla\delta_V = 0 d\Omega
~~~ \mbox{ for all } \delta_V \mbox{ satisfying } \delta_V = 0 \mbox{ on the
left and right faces}, \\
+ &\ds \int_{\Omega} \bar{\sigma}(u):\bar{\varepsilon}(\delta_u)d\Omega =
\int_{\Gamma_N} F\cdot \delta_u d\Gamma ~~~ \mbox{ for all } \delta_{u} \mbox{
satisfying } \delta_u = 0 \mbox{ on the left face},
where :math:`\delta_{\theta}, \delta_V, \delta_u` are the test functions
corresponding to :math:`\theta, V, u`, respectively, :math:`\Gamma_N` denotes
the right boundary where the density of force :math:`F` is applied and
:math:`\bar{\sigma}:\bar{\varepsilon}` is the Frobenius scalar product between
second order tensors.