# An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model

@article{AcostaSoba2021AnUD, title={An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model}, author={Daniel Acosta-Soba and Francisco Guill'en-Gonz'alez and Jos'e Rafael Rodr'iguez-Galv'an}, journal={ArXiv}, year={2021}, volume={abs/2111.07313} }

The design of numerical approximations of the Cahn-Hilliard model preserving the maximum principle is a challenging problem, even more if considering additional transport terms. In this work, we present a new upwind discontinuous Galerkin scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the maximum principle and prevents non-physical spurious oscillations. Furthermore, we show some numerical experiments in agreement with the previous theoretical results…

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## References

SHOWING 1-10 OF 40 REFERENCES

### A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging

- MathematicsComputational Geosciences
- 2018

A numerical method is formulated for the solution of the advective Cahn–Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on…

### Discontinuous Galerkin Finite Element Approximation of the Cahn-Hilliard Equation with Convection

- MathematicsSIAM J. Numer. Anal.
- 2009

The construction and convergence analysis of a discontinuous Galerkin finite element method for the Cahn-Hilliard equation with convection using discontinuous piecewise polynomials and backward Euler discretization in time is shown.

### Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation

- MathematicsArXiv
- 2021

Finite-volume schemes for the Cahn-Hilliard equation are proposed that unconditionally and discretely satisfy the boundedness of the phase field and the free-energy dissipation and can be extended to an arbitrary number of dimensions.

### A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows

- MathematicsJ. Comput. Phys.
- 2022

### Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model

- PhysicsAdv. Comput. Math.
- 2020

This paper rigorously prove the mass conservation property and the discrete energy dissipation for the proposed fully discrete discontinuous finite volume element scheme.

### Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation

- Computer ScienceJ. Comput. Appl. Math.
- 2021

### Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn–Hilliard equation

- Computer Science
- 2020

### An efficient numerical algorithm for solving viscosity contrast Cahn-Hilliard-Navier-Stokes system in porous media

- Computer ScienceJ. Comput. Phys.
- 2020

### The Cahn–Hilliard equation and some of its variants

- Mathematics
- 2017

Our aim in this article is to review and discuss the Cahn–Hilliard equation, as well as someof its variants. Such variants have applications in, e.g., biology and image inpainting.

### Phase-Field Models for Multi-Component Fluid Flows

- Mathematics
- 2012

In this paper, we review the recent development of phase-field models and their numerical methods for multi-component fluid flows with interfacial phenomena. The models consist of a Navier-Stokes…