Volume 10, Issue 3
A New Fictitious Domain Method for Elliptic Problems with the Third Type Boundary Conditions
10.4208/aamm.OA-2017-0193

Adv. Appl. Math. Mech., 10 (2018), pp. 634-651

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• Abstract

In this article, we discuss a modified least--squares/fictitious domain method for the solution of linear elliptic boundary value problems with the third type of boundary conditions (Robin boundary conditions). Let $\Omega$ and $\omega$ be two bounded domains of $\mathbb{R}^{d}$ such that $\overline{\omega} \subset \Omega$. For a linear elliptic problem in $\Omega\setminus \overline{\omega}$ with Robin boundary conditions on the boundary $\gamma$ of $\omega$, we accelerate the original least--squares/fictitious domain method in Glowinski & He [1] and present a modified least--squares formulation. This method is still a virtual control type and relies on a least-squares formulation, which makes the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results show that our method costs much less iterations and the optimal order of convergence is obtained.

• History

Published online: 2018-10

• Keywords