A nonconforming immersed finite element method for elliptic interface problems
Provides a new numerical method for solving elliptic interface problems without penalty stabilization, improving error bounds for problems with discontinuous coefficients.
Developed a nonconforming immersed finite element method for elliptic interface problems with discontinuous diffusion coefficients, achieving error estimates better than O(h√|log h|) in energy norm and O(h²|log h|) in L2 norm, confirmed by numerical results.
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.