Name
Abstract | ||
|---|---|---|
We propose and analyze a semi-discrete and a fully discrete mixed finite element method for the Cahn-Hilliard equation ut + Δ(ɛΔu−ɛ−1f(u)) = 0, where ɛ 0 is a small parameter. Error estimates which are quasi-optimal order in time and optimal order in space are shown for the proposed methods under minimum regularity assumptions on the initial data and the domain. In particular, it is shown that all error bounds depend on ** only in some lower polynomial order for small ɛ. The cruxes of our analysis are to establish stability estimates for the discrete solutions, to use a spectrum estimate result of Alikakos and Fusco [2], and Chen [15] to prove a discrete counterpart of it for a linearized Cahn-Hilliard operator to handle the nonlinear term on a stretched time grid. The ideas and techniques developed in this paper also enable us to prove convergence of the fully discrete finite element solution to the solution of the Hele-Shaw (Mullins-Sekerka) problem as ɛ → 0 in [29]. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1007/s00211-004-0546-5 | Numerische Mathematik |
Keywords | Field | DocType |
mixed finite element method,lower polynomial order,error estimate,cahn-hilliard equation ut,optimal order,discrete mixed finite element,error analysis,discrete counterpart,error bound,discrete solution,quasi-optimal order,discrete finite element solution,spectrum,cahn hilliard equation | Convergence (routing),Nonlinear system,Polynomial,Mathematical analysis,Cahn–Hilliard equation,Finite element method,Numerical analysis,Numerical stability,Mathematics,Mixed finite element method | Journal |
Volume | Issue | ISSN |
99 | 1 | 0945-3245 |
Citations | PageRank | References |
39 | 8.54 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiaobing Feng | 1 | 906 | 112.55 |
| Andreas Prohl | 2 | 302 | 67.29 |