A class of nonconforming immersed finite element methods for Stokes interface problems

In this paper, we introduce a class of lowest-order nonconforming immersed finite element (IFE) methods for solving two-dimensional Stokes interface problems. The proposed methods do not require the solution mesh to align with the fluid interface and can use either triangular or rectangular meshes. On triangular meshes, the Crouzeix–Raviart element is used for velocity approximation, and piecewise constant for pressure. On rectangular meshes, the Rannacher–Turek rotated Q1 - Q0 finite element is used. The new vector-valued IFE functions are constructed to approximate the interface jump conditions. Basic properties including the unisolvency and the partition of unity of these new IFE functions are discussed. Approximation capabilities of the new IFE spaces for the Stokes interface problems are examined through a series of numerical examples. Numerical approximations in the L2 -norm and the broken H1 -norm for the velocity and the L2 -norm for the pressure are observed to converge optimally.