Numerical analysis of a steepest-descent pde model for surface relaxation below the roughening temperature

R. V. Kohn, H. M. Versieux

Research output: Contribution to journalArticle

Abstract

We study the numerical solution of a PDE describing the relaxation of a crystal surface to a flat facet. The PDE is a singular, nonlinear, fourth order evolution equation, which can be viewed as the gradient flow of a convex but nonsmooth energy with respect to the H per -1 inner product. Our numerical scheme uses implicit discretization in time and a mixed finite element approximation in space. The singular character of the energy is handled using regularization, combined with a primal-dual method. We study the convergence of this scheme, both theoretically and numerically.

Original languageEnglish (US)
Pages (from-to)1781-1800
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number5
DOIs
StatePublished - 2010

Keywords

  • Crystal growth
  • Galerkin approximation
  • H steepest descent
  • Mixed finite element methods
  • Surface relaxation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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