Optimal-order error bounds of order h^2 plus tau^q are proven for the fully discrete bulk-surface Cahn-Hilliard system with dynamic boundary conditions for BDF methods q=1,...,5, using an almost mass conservation argument.
A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential
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abstract
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish optimal order error bounds for a (fully implicit) backward Euler time-discretisation, and an implicit-explicit time-discretisation, with isoparametric surface finite elements discretising space.
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Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
Optimal-order error bounds of order h^2 plus tau^q are proven for the fully discrete bulk-surface Cahn-Hilliard system with dynamic boundary conditions for BDF methods q=1,...,5, using an almost mass conservation argument.