A Linearity Preserving Algebraic Flux Correction Scheme of Upwind Type Satisfying the Discrete Maximum Principle on Arbitrary Meshes
Various choices of limiters in the framework of algebraic flux correction (AFC) schemes applied to the numerical solution of scalar steady-state convection–diffusion–reaction equations are discussed. A new limiter of upwind type is proposed for which the AFC scheme satisfies the discrete maximum principle and linearity preservation property on arbitrary meshes.
This work has been supported through the grant No. 16-03230S of the Czech Science Foundation.
- 5.P. Knobloch, On the application of algebraic flux correction schemes to problems with non-vanishing right-hand side. Boundary and Interior Layers, Computational and Asymptotic Methods – BAIL 2014, ed. by P. Knobloch. Lect. Notes Comput. Sci. Eng., vol. 108 (Springer, Berlin, 2015), pp. 99–109Google Scholar
- 6.P. Knobloch, On the discrete maximum principle for algebraic flux correction schemes with limiters of upwind type. Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016, ed. by Z. Huang, M. Stynes, and Z. Zhang. Lect. Notes Comput. Sci. Eng., vol. 120 (Springer, Berlin, 2017), pp. 129–139Google Scholar
- 7.D. Kuzmin, Algebraic flux correction for finite element discretizations of coupled systems, in Proceedings of the International Conference on Computational Methods for Coupled Problems in Science and Engineering, ed. by M. Papadrakakis, E. Oñate, B. Schrefler (CIMNE, Barcelona, 2007), pp. 1–5Google Scholar