A MultiMesh Finite Element Method for the Stokes Problem
This work enables flow simulations on complex geometries composed of overlapping meshes, which is a first step toward practical flow applications.
The paper extends the multimesh finite element method to the Stokes problem, achieving optimal convergence rates by stabilizing cut elements with a consistent least-squares term.
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function space with interface conditions enforced by means of Nitsche's method. In this contribution, we consider the Stokes problem as a first step towards flow applications. The multimesh formulation leads to so called cut elements in the underlying meshes close to overlaps. These demand stabilization to ensure coercivity and stability of the stiffness matrix. We employ a consistent least-squares term on the overlap to ensure that the inf-sup condition holds. We here present the method for the Stokes problem, discuss the implementation, and verify that we have optimal convergence.