Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions

2024/07/30 by Bullerjahn, Nils, Kovács, Balázs
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2407.20698

Abstract

A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type 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 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system.

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