249 RWTH Publication No: 47268        2005        IGPM249.pdf
TITLE A Smoothness Preserving Fictitious Domain Method for Elliptic Boundary Value Problems
AUTHORS Mario S. Mommer
ABSTRACT We introduce a new fictitious domain method for the solution of second order elliptic boundary value problems with Dirichlet or Neumann boundary conditions on domains with C2 boundary. The main advantage of this method is that it extends the solutions smoothly, which leads to better performance by achieving higher accuracy with less degrees of freedom. The method is based on a least-squares interpretation of the fundamental requirements that the solution produced by a fictitious domain method should satisfy. Careful choice of discretization techniques, together with a special solution strategy lead then to smooth solutions of the resulting underdetermined problem. Numerical experiments are provided which illustrate the performance and of the approach.
KEYWORDS boundary value problems, fictitious domain methods, convergence rates, wavelets
DOI 10.1093/imanum/dri045
PUBLICATION IMA Journal of Numerical Analysis, Volume 26, Issue 3, July 2006, Pages 503–524