Fix documentation misprint, modulus should be norm. #14367
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simonsticko
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peterrum
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Oct 23, 2022
Realized I missed something,,, Converted to draft in the meantime. |
bangerth
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Oct 25, 2022
| * \int_{S\cap F} f |d\bar{r}| = | ||
| * \int_{\hat{S}\cap\hat{F}} f \circ F_{K} | J d\hat{r}| | ||
| * \approx \sum_{q} f \left(F_{K}(\hat{x}_{q}) \right) |J_q \hat{t}_q| w_q, | ||
| * \int_{S\cap F} f \|d\bar{r}\| = |
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That's not quite right -- dr is an area or volume element, and as such is a scalar. Depending on how you define the transformation, it may be positive or negative, and so using |...| makes sense. But it isn't a vector.
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Sorry for not fixing this sooner... No, I really do mean the vector here, but I realized that my notation was strange, so I rewrote this. Updated now.
| * \int_{\hat{S}\cap\hat{F}} f \circ F_{K} | J d\hat{r}| | ||
| * \approx \sum_{q} f \left(F_{K}(\hat{x}_{q}) \right) |J_q \hat{t}_q| w_q, | ||
| * \int_{S\cap F} f \|d\bar{r}\| = | ||
| * \int_{\hat{S}\cap\hat{F}} f \circ F_{K} \| J d\hat{r} \| |
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| * \approx \sum_{q} f \left(F_{K}(\hat{x}_{q}) \right) \|J(\hat{x}_q) | ||
| * \hat{t}_q \| w_q, |
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But I think this here would then be correct.
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Ping? |
simonsticko
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Text now: |
bangerth
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Apr 10, 2023
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OK, that makes sense. Thanks! |
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