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Commit 4fd6dc56 authored by Martin Schneider's avatar Martin Schneider Committed by Timo Koch
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[ex][model][slides] Update slides

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...@@ -11,7 +11,7 @@ A DuMu^x^ model is an implementation of a discretized **mathematical model**, ge ...@@ -11,7 +11,7 @@ A DuMu^x^ model is an implementation of a discretized **mathematical model**, ge
Mathematical model (PDE): Mathematical model (PDE):
$$ $$
\begin{aligned} \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} \end{aligned}
$$ $$
...@@ -71,12 +71,7 @@ $$ ...@@ -71,12 +71,7 @@ $$
\end{aligned} \end{aligned}
$$ $$
with <img src=img/box_scv_scvf.png width="80%">
- $c_B^n:$ 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)
## Example: Diffusion equation ## Example: Diffusion equation
Discrete model using the Box discretization: Discrete model using the Box discretization:
...@@ -87,7 +82,12 @@ $$ ...@@ -87,7 +82,12 @@ $$
\end{aligned} \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` ## `LocalResidual`
The local residual of the diffusion model: The local residual of the diffusion model:
......
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