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A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential (2405.11984v1)

Published 20 May 2024 in math.NA and cs.NA

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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