Error control for the approximation of Allen--Cahn and Cahn--Hilliard equations with a logarithmic potential
- Bartels, Sören
- Müller, Rüdiger
2010 Mathematics Subject Classification
- 65M60 65M15 35K55
- Allen-Cahn equation, Cahn-Hilliard equation, logarithmic potential, finite element method, error analysis, adaptive methods
A fully computable upper bound for the finite element approximation error of Allen-Cahn and Cahn-Hilliard equations with logarithmic potentials is derived. Numerical experiments show that for the sharp interface limit this bound is robust past topological changes. Modifications of the abstract results to derive quasi-optimal error estimates in different norms for lowest order finite element methods are discussed and lead to weaker conditions on the residuals under which the conditional error estimates hold.
- Numer. Math., 119 (2011) pp. 409--435.