Error estimates of fully discrete finite element solutions for the 2D Cahn–Hilliard equation with infinite time horizon

Abstract

In this article, we deal with a rigorous error analysis for the finite element solutions of the two‐dimensional Cahn–Hilliard equation with infinite time. The L 2 − H 1 error estimates with respect to ( h , τ ) are proven for the fully discrete conforming piecewise linear element solution under Assumption (A1) on the initial value and Assumption (A2) on the discrete spectrum estimate in the finite element space. The analysis is based on sharp a‐priori estimates for the solutions, particularly reflecting their behavior as t → ∞ . Numerical experiments are carried out to support the theoretical analysis and demonstrate the efficiency of the fully discrete mixed finite element methods. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 742–762, 2017

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