The shifted Nitsche method: A new approach to embedded boundary conditions

Embedded boundary methods obviate the need for continual re-meshing in many applications involving rapid prototyping and design. Unfortunately, many finite element embedded boundary methods for incompressible flow are also difficult to implement due to the need to perform complex cell-cutting operations at boundaries. We present a new, stable, and simple embedded boundary method, which we call the shifted Nitsche method. The proposed method eliminates the need to perform cell cutting, and demonstrate it on large-scale incompressible flow problems, solid mechanics, shallow water flows.