Derives a bulk-surface phase-field model for two-phase Navier-Stokes flow in a moving domain with dynamic contact angles and generalized slip, obtained from mass balance via Lagrange multipliers and energetic variational methods, generalizing prior static-boundary models.
Bullerjahn
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abstract
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy estimate and the novel approach of exploiting the almost mass conservation of the error equations to derive a Poincar\'e-type inequality. We demonstrate how this approach can be generalized to other almost mass conserving problems. To this end we prove optimal-order fully discrete error estimates for the Cahn--Hilliard equation on evolving surfaces. We illustrate and complement our findings by numerical experiments.
verdicts
UNVERDICTED 2representative citing papers
Proof of optimal H1-norm error estimates for A-stable BDF1/BDF2 full discretizations of Willmore flow using surface finite elements of degree at least 2.
citing papers explorer
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A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Bulk-Surface Interaction
Derives a bulk-surface phase-field model for two-phase Navier-Stokes flow in a moving domain with dynamic contact angles and generalized slip, obtained from mass balance via Lagrange multipliers and energetic variational methods, generalizing prior static-boundary models.
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Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces
Proof of optimal H1-norm error estimates for A-stable BDF1/BDF2 full discretizations of Willmore flow using surface finite elements of degree at least 2.