author = {Clarenz, U. and Diewald, U. and Dziuk, G. and Rumpf, M. and Rusu,
  title = {A finite element method for surface restoration with smooth boundary
  journal = {Computer Aided Geometric Design},
  year = {2004},
  volume = {21},
  pages = {427--445},
  number = {5},
  abstract = {In surface restoration usually a damaged region of a surface has to
	be replaced by a surface patch which restores the region in a suitable
	way. In particular one aims for $C^1$-continuity at the patch boundary.
	The Willmore energy is considered to measure fairness and to allow
	appropriate boundary conditions to ensure continuity of the normal
	field. The corresponding $L^2$-gradient flow as the actual restoration
	process leads to a system of fourth order partial differential equations,
	which can also be written as system of two coupled second order equations.
	As it is well--known, fourth order problems require an implicit time
	discretization. Here a semi--implicit approach is presented which
	allows large timesteps. For the discretization of the boundary condition,
	two different numerical methods are introduced. Finally, we show
	applications to different surface restoration problems.},
  pdf = { 1}