Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids

Gosse, Laurent

doi:10.1090/mcom/3451

Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids
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Math. Comp. 89 (2020), 139-168 Request permission

Abstract:

A notion of “2D well-balanced” for drift-diffusion is proposed. Exactness at steady-state, typical in 1D, is weakened by aliasing errors when deriving “truly 2D” numerical fluxes from local Green’s function. A main ingredient for proving that such a property holds is the optimality of the trapezoidal rule for periodic functions. In accordance with practical evidence, a “Bessel scheme” previously introduced in [SIAM J. Numer. Anal. 56 (2018), pp. 2845–2870] is shown to be “2D well-balanced” (along with former algorithms known as “discrete weighted means” or “tailored schemes”. Some $L^2$ stability estimates are established, too.

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