Bänsch E, Morin P, Nochetto R (2004)
Publication Type: Journal article, Original article
Publication year: 2004
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 42
Pages Range: 773-799
Journal Issue: 2
DOI: 10.1137/S0036142902419272
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 verification 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 in finite time, such as infinite slopes and cracks. © 2004 Society for Industrial and Applied Mathematics.
APA:
Bänsch, E., Morin, P., & Nochetto, R. (2004). Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation. SIAM Journal on Numerical Analysis, 42(2), 773-799. https://doi.org/10.1137/S0036142902419272
MLA:
Bänsch, Eberhard, Pedro Morin, and Ricardo Nochetto. "Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation." SIAM Journal on Numerical Analysis 42.2 (2004): 773-799.
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