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Simula Research Laboratory

Upwind DG property-preserving scheme for convection equations: applicatons to Cahn-Hilliard model

Authors
Affiliations
Universidad de Cádiz
Universidad de Cádiz
Universidad de Sevilla

We present an upwind Discontinuous Galerkin discrete scheme for conservation laws, for which existence of solutions and properties like positivty or maximum principle can be proven. Furthermore, we show how this scheme can be extended to more complex non-linear convection equations, specifcally to the convective Cahn-Hilliard model with degenerate mobility, preserving the maximum principle and preventing non-physical spurious oscillations. Furthermore, we show some numerical experiments in agreement with the previous theoretical results and also some comparisons

References

Acosta-Soba, D., Guillén-González, F., & Rodríguez-Galván, J. R. (2023). An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model. Numerical Algorithms, 92(3), 1589-1619.

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