JournalsifbVol. 8 , No. 1DOI 10.4171/ifb/134

Error analysis of a finite element method for the Willmore flow of graphs

  • Gerhard Dziuk

    Universität Freiburg, Germany
  • Klaus Deckelnick

    Otto-von-Guericke-Universität Magdeburg, Germany
Error analysis of a finite element method for the Willmore flow of graphs cover

Abstract

The evolution of two--dimensional graphs under Willmore flow is approximated by a continuous--in--time finite element method. The highly nonlinear fourth order problem is split into two coupled second order problems using height and a weighted mean curvature as variables. We prove a--priori error estimates for the resulting time--continuous scheme and present results of test calculations.