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I am looking for possible numerical methods to solve the PDE $$u_t+c u_x= \frac{-c}{x}u$$

I am particularly interested in a Finite elements method, although I am also curious if you can expose some other methods.

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    $\begingroup$ It looks like there is an analytic solution here, if that's of interest. $\endgroup$
    – Maxim Umansky
    Jun 20, 2022 at 19:40
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    $\begingroup$ Specifically, you can use the method of characteristics I assume. But you need to state the domain of possible $x$ values, and what you want to happen at $x=0$. $\endgroup$
    – Wolfgang Bangerth
    Jun 21, 2022 at 0:48

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