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Finite volume schemes for multilayer diffusion. (arXiv:1711.10052v2 [math.NA] UPDATED)
来源于:arXiv
This paper focusses on finite volume schemes for solving multilayer diffusion
problems. We develop a finite volume method that addresses a deficiency of
recently proposed finite volume/difference methods, which consider only a
limited number of interface conditions and do not carry out stability or
convergence analysis. Our method also retains second order accuracy in space
while preserving the tridiagonal matrix structure of the classical single-layer
discretisation. Stability and convergence analysis of the new finite volume
method is presented for each of the three classical time discretisation
methods: forward Euler, backward Euler and Crank-Nicolson. We prove that both
the backward Euler and Crank-Nicolson schemes are always unconditionally
stable. The key contribution of the work is the presentation of a set of
sufficient stability conditions for the forward Euler scheme. Here, we find
that to ensure stability of the forward Euler scheme it is not sufficient that
the time step $\ 查看全文>>