author = {Preusser, Tobias and Rumpf, Martin and Sauter, Stefan and Schwen,
	Lars Ole},
  title = {3{D} Composite Finite Elements for Elliptic Boundary Value Problems
	with Discontinuous Coefficients},
  journal = {SIAM Journal on Scientific Computing},
  year = {2011},
  volume = {33},
  pages = {2115--2143},
  number = {5},
  abstract = {For scalar and vector-valued elliptic boundary value problems with
	discontinuous coefficients across geometrically complicated interfaces,
	a composite finite element approach is developed. Composite basis
	functions are constructed, mimicking the expected jump condition
	for the solution at the interface in an approximate sense. The construction
	is based on a suitable local interpolation on the space of admissible
	functions. We study the order of approximation and the convergence
	properties of the method numerically. As applications, heat diffusion
	in an aluminum foam matrix filled with polymer and linear elasticity
	of micro-structured materials, in particular specimens of trabecular
	bone, are investigated. Furthermore, a numerical homogenization approach
	is developed for periodic structures and real material specimens
	which are not strictly periodic but are considered as statistical
	prototypes. Thereby, effective macroscopic material properties can
	be computed.},
  doi = {10.1137/100791750},
  pdf = { 1}