ANALYSIS OF ALGEBRAIC FLUX CORRECTION SCHEMES

作者：Barrenechea Gabriel R^*; John Volker; Knobloch Petr

来源：SIAM Journal on Numerical Analysis, 2016, 54(4): 2427-2451.

DOI：10.1137/15M1018216

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

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.

• 出版日期2016