A nonconforming immersed finite element method for elliptic interface problems

Abstract

A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated Q1 nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin method is employed in this IFE method without any penalty stabilization term. Error estimates in energy and L2 norms are proved to be better than $O(h\sqrt{|\log h|})$ and $O(h^2|\log h|)$, respectively, where the logarithm factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.

References in corpus (5)

• Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems
• A Group of Immersed Finite Element Spaces For Elliptic Interface Problems
• Superconvergence of Immersed Finite Element Methods for Interface Problems
• Nonconforming Immersed Finite Element Spaces For Elliptic Interface Problems
• A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods

Cited by in corpus (5)

• Solving Three-Dimensional Interface Problems with Immersed Finite Elements: A-Priori Error Analysis
• A stabilized nonconforming Nitsche's extended finite element method for Stokes interface problems
• Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems
• A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domains and Triple-Junction Points
• PIFE-PIC: Parallel Immersed-Finite-Element Particle-In-Cell For 3-D Kinetic Simulations of Plasma-Material Interactions