A partially penalty immersed Crouzeix-Raviart finite element method for interface problems

摘要: The elliptic equations with discontinuous coefficients are often used to describe the problems of multiple materials or fluids different densities conductivities diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which diffusion coefficient is piecewise definite-positive matrix. standard linear Crouzeix-Raviart type space non-interface elements and (IFE) constructed interface elements. functions satisfying jump conditions uniquely determined by integral averages edges as degrees freedom. PIFE scheme given based symmetric, nonsymmetric incomplete interior Galerkin formulation. solvability proved optimal error estimates energy norm obtained. Numerical experiments presented confirm our theoretical analysis show that newly developed has optimal-order convergence $L^{2}$ well. addition, numerical examples also indicate valid both isotropic problems.