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I'm currently studying a numerical scheme which preserves the divergence through time, i.e $div(A^{n+1}) = div(A^{n})$ where $A$ any vector field in $\mathbb{R}^n$ and $n, n+1$ time stations. This is true in Cartesian coordinates but I was wondering if it could be altered using other kind of coordinate systems, I guess not (using a diffeorphism as a coordinate transform) but what's the theoretical background ?

Thx

Amzocks
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  • Fluid dynamics or Electromagnetics? If spatially it is finite difference, no hope. If it is finite element, definitely possible, if you mean you need to have a globally well-defined divergence. – Shuhao Cao Jul 26 '13 at 15:17
  • Electromagnetism and I'm using a DG method (discontinuous Galerkin). As I switched from Cartesian to Cylindrical coordinate system, I also decomposed my fields ($\mathbf{E}$, $\mathbf{B}$) in Fourier series s.t, $\mathbf{B}(r, \phi, z) = \sum_\alpha \mathbf{\hat{B}}^\alpha(r, \phi)e^{i\alpha\phi}$. And I'd like to bring out the divergence property for the $\phi$-free fields $\mathbf{\hat{E}}$, $\mathbf{\hat{b}}$. – Amzocks Jul 29 '13 at 08:12

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