Timeline for stability of parabolic problems where nonhomogeneous term in $L^2(0,T; H^{-1}(\Omega))$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 1, 2017 at 1:46 | comment | added | Ariel So | @Jean Duchon Thanks for your suggestion. It really needs $f\in L^2（0，T; L^2(\Omega))$ to complete the proof of stability result. The assumption $f\in L^2(0,T; H^{-1}(\Omega))$ is not enough. | |
| Oct 24, 2017 at 13:15 | comment | added | Jean Duchon | I suggest you forget the finite element approximation and focus on the time discretization alone. I also suggest that you write explicitly $\partial_\tau u^n=(u^n-u^{n-1})/\tau$. I wouldn't be surprised if the stability you expect needed $f\in L^2(O,T;L^2)$. | |
| Oct 24, 2017 at 4:03 | comment | added | Ariel So | I am following a proof where $f$ is assumed to be in the space $L^2(0,T; L^2(\Omega))$ , I have presented the proof in the following link. dropbox.com/s/n5j0k6kr3rmgq2a/Proof%20.pdf?dl=0 | |
| Oct 24, 2017 at 3:51 | history | edited | Ariel So | CC BY-SA 3.0 |
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| Oct 24, 2017 at 2:43 | review | First posts | |||
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| Oct 24, 2017 at 2:39 | history | asked | Ariel So | CC BY-SA 3.0 |