A flux preserving immersed nonconforming finite element method for elliptic problems

作者：Jeon Youngmok^*; Kwak Do Young

来源：Applied Numerical Mathematics, 2014, 81: 94-104.

DOI：10.1016/j.apnum.2013.11.007

• Immersed finite element
• Hybridization
• Symmetrization

An immersed nonconforming finite element method based on the flux continuity on intercell boundaries is introduced. The direct application of flux continuity across the support of basis functions yields a nonsymmetric stiffness system for interface elements. To overcome non-symmetry of the stiffness system we introduce a modification based on the Riesz representation and a local postprocessing to recover local fluxes. This approach yields a P-1 immersed nonconforming finite element method with a slightly different source term from the standard nonconforming finite element method. The recovered numerical flux conserves total flux in arbitrary sub-domain. An optimal rate of convergence in the energy norm is obtained and numerical examples are provided to confirm our analysis.

• 出版日期2014-7