Minimal stencil finite volume scheme with the discrete maximum principle

被引：71

作者：

Lipnikov, K. ^{[2
]}

Svyatskiy, D. ^{[2
]}

Vassilevski, Yu. ^{[1
]}

机构：

[1] Inst Numer Math, Moscow 119333, Russia

[2] Los Alamos Natl Lab, Los Alamos, NM 87545 USA

来源：

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2012年 / 27卷 / 04期

关键词：

ADVECTION-DIFFUSION EQUATIONS; APPROXIMATIONS; MONOTONICITY;

D O I：

10.1515/rnam-2012-0020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a cell-centered finite volume (FV) scheme with the minimal stencil formed by the closest neighbouring cells. The discrete solution satisfies the discrete maximum principle and approximates the exact solution with second-order accuracy. The coefficients in the FV stencil depend on the solution; therefore, the FV scheme is nonlinear. The scheme is applied to a steady state advection-diffusion equation discretized on a general polygonal mesh.

引用

页码：369 / 385

页数：17

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