Controllability properties for elliptic systems, the fictitious domain method and optimal shape design problems
Dan Tiba · Birkhäuser Basel eBooks · 1992
The fictitious domain method is used in the numerical solution of partial differential equations in exterior domains or in order to apply finite differences to systems defined in domains with a complicated geometry. The principle of this approach is very useful in problems with unknown or variable domains. Taking into account certain exact controllability properties for linear or nonlinear elliptic equations, we develop an approximation method for optimal design problems by distributed control problems in a fixed domain.