ANALYSIS OF ALGEBRAIC FLUX CORRECTION SCHEMES

被引：50

作者：

Barrenechea, Gabriel R. ^{[1
]}

John, Volker ^{[2
,3
]}

Knobloch, Petr ^{[4
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[2] Weierstrass Inst Appl Anal & Stochast WIAS, D-10117 Berlin, Germany

[3] Free Univ Berlin, Dept Math & Comp Sci, D-14195 Berlin, Germany

[4] Charles Univ Prague, Fac Math & Phys, Dept Numer Math, Prague 18675 8, Czech Republic

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 04期

关键词：

algebraic flux correction method; linear boundary value problem; well-posedness; discrete maximum principle; convergence analysis; convection-diffusion-reaction equations; ACCELERATION; DESIGN;

D O I：

10.1137/15M1018216

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A family of algebraic flux correction (AFC) schemes for linear boundary value problems in any space dimension is studied. These methods' main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection-diffusion-reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.

引用

页码：2427 / 2451

页数：25

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