Timeline for Bounding the determinant of the Jacobian between a set and its polyhedral approximation
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S yesterday | history | edited | David Gao | CC BY-SA 4.0 |
Fixed math typesetting (\partial for the boundary, \mathbb{R} for real numbers, \| \| for norms) and a typo in the text.
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| S yesterday | history | suggested | MathMax | CC BY-SA 4.0 |
Fixed math typesetting (\partial for the boundary, \mathbb{R} for real numbers, \| \| for norms) and a typo in the text.
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| yesterday | review | Suggested edits | |||
| S yesterday | |||||
| Mar 5, 2020 at 18:09 | answer | added | MathMax | timeline score: 2 | |
| Nov 25, 2016 at 9:53 | history | edited | Josiki | CC BY-SA 3.0 |
added 74 characters in body
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| Nov 24, 2016 at 10:04 | comment | added | Josiki | 1) Good point about $J$ not being constant, little oversight. I guess I mean something like $||J-1||^2){L^2 \Omega or \Omega_h} \leq C_2h^2$. 2) Also a good point. I guess my question is if there exists such a map $\omega$ such that the Jacobian has this property. I think it must be true, as if $\Omega$ and $\Omega_h$ are sufficiently close then the Jacobian will almost be the identity. | |
| Nov 23, 2016 at 14:38 | comment | added | Liviu Nicolaescu | 1). What kind of bounds are you looking for when you write $|J-1|$? $J$ is not constant: it depends on $x\in\Omega_h$. 2). I am inclined to believe that no such bounds exist because there exist many diffeomorphisms $\Omega\to\Omega$ that are the identity on $\partial \Omega$. (Take a smooth vector field on $\Omega$ that vanishes on $\partial \Omega$. The flow of $X$ will generate many such diffeomorphisms.) | |
| Nov 23, 2016 at 14:15 | review | First posts | |||
| Nov 23, 2016 at 14:18 | |||||
| Nov 23, 2016 at 14:15 | history | asked | Josiki | CC BY-SA 3.0 |