1D ODE with non-constant coefficients.

[ethrelfall]

Dear community,

I've been trying to set up a very simple example of a 1D ODE in weak form. The equation contains the radial part of the scalar Laplacian in 2D and so there are metric scale factors giving non-constant coefficients.

I have implemented something that I think is plausible but it doesn't give the correct solution. The (very short) script and the problem are explained at https://github.com/ethrelfall/further-Firedrake.

Please, is someone able to say how to do this properly?

(Search for matching discussions returned nowt.)

Thanks!

[colinjcotter]

Code looks ok at a glance. Are you comparing with the exact solution applied to w, not the coordinate, by any chance?

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________________________________________ From: ethrelfall ***@***.***> Sent: 13 December 2022 17:19 To: firedrakeproject/firedrake Cc: Subscribed Subject: [firedrakeproject/firedrake] 1D ODE with non-constant coefficients. (Discussion #2686) Dear community, I've been trying to set up a very simple example of a 1D ODE in weak form. The equation contains the radial part of the scalar Laplacian in 2D and so there are metric scale factors giving non-constant coefficients. I have implemented something that I think is plausible but it doesn't give the correct solution. The (very short) script and the problem are explained at https://github.com/ethrelfall/further-Firedrake. Please, is someone able to say how to do this properly? (Search for matching discussions returned nowt.) Thanks! — Reply to this email directly, view it on GitHub<#2686>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4WJWQTC6TMYUUDYXCTWNCV2TANCNFSM6AAAAAAS5O3MTI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[colinjcotter]

Oh, I see the problem. Your RHS is v*w*dx but it should be q*v*dx where q is set to -1.

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________________________________________ From: Cotter, Colin J ***@***.***> Sent: 13 December 2022 18:50 To: firedrakeproject/firedrake Subject: Re: [firedrakeproject/firedrake] 1D ODE with non-constant coefficients. (Discussion #2686) Code looks ok at a glance. Are you comparing with the exact solution applied to w, not the coordinate, by any chance?

________________________________________ From: ethrelfall ***@***.***> Sent: 13 December 2022 17:19 To: firedrakeproject/firedrake Cc: Subscribed Subject: [firedrakeproject/firedrake] 1D ODE with non-constant coefficients. (Discussion #2686) Dear community, I've been trying to set up a very simple example of a 1D ODE in weak form. The equation contains the radial part of the scalar Laplacian in 2D and so there are metric scale factors giving non-constant coefficients. I have implemented something that I think is plausible but it doesn't give the correct solution. The (very short) script and the problem are explained at https://github.com/ethrelfall/further-Firedrake. Please, is someone able to say how to do this properly? (Search for matching discussions returned nowt.) Thanks! — Reply to this email directly, view it on GitHub<#2686>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4WJWQTC6TMYUUDYXCTWNCV2TANCNFSM6AAAAAAS5O3MTI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[ethrelfall]

Thanks so much for taking a look. But why should I NOT have \int r v dx on the RHS (wh. w=r in the script), as in the formula in the readme - ?

[ksagiyam]

Your analytical solution is not correct; if I add a correction term to your rhs as in L = ((w+1.5/w**2)*v)*dx, what you wrote down becomes the exact solution.

[ethrelfall]

Ah you're right, I see I used 1/r in the analytic solution when it should have been ln r ... oops! Thanks v. much.

[colinjcotter]

oh ah you multiplied through by r! sorry! On 13 Dec 2022, at 18:54, ethrelfall ***@***.***> wrote:  Thanks so much for taking a look. But why should I NOT have \int r v dx on the RHS (wh. w=r in the script), as in the formula in the readme - ? — Reply to this email directly, view it on GitHub<#2686 (reply in thread)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ABOSV4UO3RTIMMREJUEIXC3WNDA43ANCNFSM6AAAAAAS5O3MTI>. You are receiving this because you commented.Message ID: ***@***.***>

[ethrelfall]

Yes then I made schoolboy error :(