From 4fd6dc5670527672438e657561a7ce484b8f5211 Mon Sep 17 00:00:00 2001
From: Martin Schneider <martin.schneider@iws.uni-stuttgart.de>
Date: Wed, 17 Jul 2024 15:32:42 +0200
Subject: [PATCH] [ex][model][slides] Update slides
---
slides/model.md | 16 ++++++++--------
1 file changed, 8 insertions(+), 8 deletions(-)
diff --git a/slides/model.md b/slides/model.md
index 8a7bccbc..e7f8dfac 100644
--- a/slides/model.md
+++ b/slides/model.md
@@ -11,7 +11,7 @@ A DuMu^x^ model is an implementation of a discretized **mathematical model**, ge
Mathematical model (PDE):
$$
\begin{aligned}
-\frac{\partial S(u)}{\partial t} + \nabla \cdot \mathbf{F}(u) = q, \quad \forall (t,\mathbf{x}) \in (0,T] \times \Omega
+\frac{\partial S(u)}{\partial t} + \nabla \cdot \mathbf{F}(u) = q(u), \quad \forall (t,\mathbf{x}) \in (0,T] \times \Omega
\end{aligned}
$$
@@ -71,12 +71,7 @@ $$
\end{aligned}
$$
-with
-
-- $c_B^n:$ concentration at time $t_n$ and control volume $B$
-- $c^n_h:$ global discrete solution at time $t_n$, interpolated using __basis functions__
-- $\mathbf{n}:$ unit outer normal vector
-- $\sigma:$ sub control volume face (scvf)
+<img src=img/box_scv_scvf.png width="80%">
## Example: Diffusion equation
Discrete model using the Box discretization:
@@ -87,7 +82,12 @@ $$
\end{aligned}
$$
-<img src=img/box_scv_scvf.png width="80%">
+with
+
+- $c_B^n:$ concentration at time $t_n$ and control volume $B$
+- $c^n_h:$ global discrete solution at time $t_n$, interpolated using __basis functions__
+- $\mathbf{n}:$ unit outer normal vector
+- $\sigma:$ sub control volume face (scvf)
## `LocalResidual`
The local residual of the diffusion model:
--
GitLab