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Mismatch between documentation and input file variable definitions in ex03_coupling #33458

Description

@GiudGiud

Problem description

See thread below and the follow up on the discussion page for more details (where the problem statements are)

How to reproduce

look at the documentation example
look at the input and figures

Impact

confusion documentation

Discussed in #33455

Originally posted by Daybyday-there July 29, 2026

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Question

I am a beginner in MOOSE. Recently, I came across some tutorials and examples. While examining example 3 (https://mooseframework.inl.gov/releases/moose/2024-11-11/getting_started/examples_and_tutorials/examples/ex03_coupling.html), I noticed that the kernel settings in the input file (ex03.i) seemed to be inconsistent with the physical equations stated in the problem description. According to the document, the equation of this example is:
$-\nabla\cdot\nabla u + \nabla v \cdot \nabla u = 0$
$-\nabla\cdot\nabla v = 0$
and the document states that the variable diffused corresponds to the physical variable $u$, and the variable convected corresponds to the physical variable $v$.
However, In the [Kernels] of ex03.i:
[./conv]
type = ExampleConvection
variable = convected
some_variable = diffused
[../]
This kernel acts on the convected (i.e., the physical variable $v$) equation, but the physical equation requires that the coupling term $\nabla v \cdot \nabla u$ should act on the equation of $u$.

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    P: minorA defect that does not affect the accuracy of results.T: defectAn anomaly, which is anything that deviates from expectations.

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