作者: Isabelle Ramière , Philippe Angot , Michel Belliard
DOI: 10.1016/J.JCP.2007.01.026
关键词: Discretization 、 Robin boundary condition 、 Dirichlet problem 、 Finite volume method 、 Boundary value problem 、 Fictitious domain method 、 Mathematics 、 Mathematical analysis 、 Dirichlet conditions 、 Neumann boundary condition
摘要: This study addresses a new fictitious domain method for elliptic problems in order to handle general and possibly mixed embedded boundary conditions (E.B.C.): Robin, Neumann Dirichlet on an immersed interface. The main interest of this is use simple structured meshes, uniform Cartesian nested grids, which do not generally fit the interface but define approximate one. A cell-centered finite volume scheme with non-conforming mesh derived solve set equations additional algebraic transmission linking both flux solution jumps through Hence, local correction devised take account relative surface ratios each control Robin or condition. Then, numerical conserves first-order accuracy respect step. opens way combine E.B.C. multilevel refinement solver increase precision vicinity Such very efficient: L^2- L^~-norm errors vary like O(h"l"*) where h"l"* grid step finest level around until residual discretization error non-refined zone reached. results reported here convection-diffusion Dirichlet, (Dirichlet Robin) confirm expected as well performances present method.