Abstract
The multimesh finite element method enables the solution of partial dif-
ferential equations on a computational mesh composed by multiple arbitrarily over-
lapping meshes. The discretization is based on a continuous–discontinuous function
space with interface conditions enforced by means of Nitsche’s method. In this con-
tribution, 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.
ferential equations on a computational mesh composed by multiple arbitrarily over-
lapping meshes. The discretization is based on a continuous–discontinuous function
space with interface conditions enforced by means of Nitsche’s method. In this con-
tribution, 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.