A New Fictitious Domain Method for Elliptic Problems with the Third Type Boundary Conditions

作者：He, Qiaolin; Lv, Xiaomin^*

来源：Advances in Applied Mathematics and Mechanics, 2018, 10(3): 634-651.

DOI：10.4208/aamm.OA-2017-0193

• Least-squares methods
• fictitious domain methods
• finite element methods
• Robin boundary conditions

In this article, we discuss amodified 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 R-d such that (omega)over bar> subset of Omega . For a linear elliptic problem in Omega\(omega) over bar 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.

• 出版日期2018-6
• 单位四川大学