An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes

Barrenechea, Gabriel R. and Volker, John and Knobloch, Petr (2017) An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes. Mathematical Models and Methods in Applied Sciences, 27 (3). pp. 525-548. ISSN 0218-2025

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    Abstract

    This work is devoted to the proposal of a new flux limiter that makes the algebraic flux correction finite element scheme linearity and positivity preserving on general simplicial meshes. Minimal assumptions on the limiter are given in order to guarantee the validity of the discrete maximum principle, and then a precise definition of it is proposed and analyzed. Numerical results for convection–diffusion problems confirm the theory.