230 RWTH Publication No: 47144        2003        IGPM230.pdf
TITLE Fictitious Domain-Lagrange Multiplier Approach: Smoothness Analysis
AUTHORS Mario S. Mommer
ABSTRACT We consider the Fictitious domain - Lagrange multiplier approach for second order elliptic boundary value problems with Dirichlet boundary conditions, and study the relation between the smoothness of the solution of the original problem and the solution of the new problem. We present lower bounds for the Besov smoothness for the general n-dimensional case in relation to the choice of the extension for the right-hand side. A numerical experiment illustrates the practical relevance of these estimates.
KEYWORDS Lagrange multipliers, boundary conditions, convergence rates, fictitious domains