A Nonconforming Finite-Element Method for the Two-Dimensional Cahn–Hilliard Equation
- 1 August 1989
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 26 (4) , 884-903
- https://doi.org/10.1137/0726049
Abstract
The Cahn–Hilliard equation is a nonlinear evolutionary equation that is fourth order in space. In this paper a continuous in-time finite-element Galerkin approximation is considered. We use the nonconforming Morley element and derive optimal order error bounds in $L^2 $.
Keywords
This publication has 8 references indexed in Scilit:
- Numerical Studies of the Cahn-Hilliard Equation for Phase SeparationIMA Journal of Applied Mathematics, 1987
- On the Cahn-Hilliard equationArchive for Rational Mechanics and Analysis, 1986
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimatesESAIM: Mathematical Modelling and Numerical Analysis, 1985
- Nonlinear aspects of the Cahn-Hilliard equationPhysica D: Nonlinear Phenomena, 1984
- On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensionsMathematics of Computation, 1983
- On nonconforming an mixed finite element methods for plate bending problems. The linear caseRAIRO. Analyse numérique, 1979
- A Priori $L_2 $ Error Estimates for Galerkin Approximations to Parabolic Partial Differential EquationsSIAM Journal on Numerical Analysis, 1973
- Non-Homogeneous Boundary Value Problems and ApplicationsPublished by Springer Nature ,1972