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Typical finite volume methods are conservative, because fluxes (of e.g., mass or energy) are always between neighboring cells. Is the same generally true for finite element codes? Do I correctly assume that implicit time stepping would then be 'globally' conservative, except for flows through the domain boundaries?

Background information: The reason I'm asking is that colleagues who use the plasma module of Comsol do not observe charge conservation in their simulations. The equations are of the following form: $$\partial_t n_1 + \nabla \cdot \vec{f} = S \, n_1\\ \partial_t n_2 = S \, n_1,$$ where $\vec{f}$ and $S$ non-linearly depend on other variables. The quantity $\int n_2 - n_1 dV$ is not conserved, but the conservation error shrinks for smaller time steps. I believe that this module internally works with $log(n)$ instead of $n$, where $n$ is the density, to avoid certain numerical problems.

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    $\begingroup$ finite element discretizations are, in general, non-conservative - as explained here. $\endgroup$
    – GoHokies
    Mar 13, 2018 at 20:11
  • $\begingroup$ Do you mean the second answer (which I don't really understand)? The first answer addresses stability. $\endgroup$ Mar 13, 2018 at 22:55

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