Name
Abstract | ||
|---|---|---|
Surface diffusion is a (fourth-order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for graphs and derive a priori error estimates for a time-continuous finite element discretization. We also introduce a semi-implicit time discretization and a Schur complement approach to solve the resulting fully discrete, linear systems. After computational veri. cation of the orders of convergence for polynomial degrees 1 and 2, we show several simulations in one dimension and two dimensions with and without forcing which explore the smoothing effect of surface diffusion, as well as the onset of singularities infinite time, such as infinite slopes and cracks. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1137/S0036142902419272 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
surface diffusion,fourth-order parabolic problem,finite elements,a priori error estimates,Schur complement,smoothing effect | Discretization,Mathematical optimization,Nonlinear system,Linear system,Mathematical analysis,Mean curvature,Finite element method,Smoothing,Mathematics,Schur complement,Laplace operator | Journal |
Volume | Issue | ISSN |
42 | 2 | 0036-1429 |
Citations | PageRank | References |
9 | 1.64 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eberhard Bänsch | 1 | 141 | 35.47 |
| Pedro Morin | 2 | 331 | 47.99 |
| Ricardo H. Nochetto | 3 | 907 | 110.08 |