= Centered Dirichlet drift-diffusion energy identity
{title2=$\operatorname{Re}\langle U,(D_2+\kappa D_1)U\rangle_d=-d^{-1}\sum_{m=0}^M|u_{m+1}-u_m|^2$}
For the centered second difference and centered first difference on a finite interval with zero <Dirichlet boundary conditions>, the diffusion <matrix> is symmetric negative definite and the drift <matrix> is <skew-symmetric>. Discrete <summation by parts> gives the displayed mesh-weighted identity. It proves contraction in the discrete <L2 norm> without needing periodic modes, positive stencil coefficients or simultaneous diagonalization.
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