Numerical Solution of Linear Elliptic Problems with Robin Boundary Conditions by a Least-Squares/Fictitious Domain Method

Abstract

Motivated by the numerical simulation of particulate flow with slip boundary conditions at the interface fluid/particles, our goal, in this publication, is to discuss a fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions. The method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results are presented; they suggest optimal orders of convergence for the finite element implementation of our fictitious domain method. A (brief) history of fictitious domain methods can be found in, e.g., [[3], Chap. 8].