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Abstract
A family of algebraic flux correction 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.
Original language  English 

Pages (fromto)  2427–2451 
Number of pages  25 
Journal  SIAM Journal on Numerical Analysis 
Volume  54 
Issue number  4 
Early online date  16 Aug 2016 
DOIs  
Publication status  Epub ahead of print  16 Aug 2016 
Keywords
 algebraic flux correction method
 linear boundary value problem
 wellposedness
 discrete maximum principle
 convergence analysis
 convection–diffusion–reaction equations
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Projects
 1 Finished

Minimal stabilization procedures on anisotropic meshes and nonlinear schemes
15/09/12 → 14/09/15
Project: Research