Manuel Solano, Felipe Vargas:
An unfitted HDG method for Oseen equations
We propose and analyze a high order unfitted hybridizable discontinuous Galerkin method to numerically solve Oseen equations in a domain having a curved boundary. The domain is approximated by a polyhedral computational domain not necessarily fitting Ω . The boundary condition is transferred to the computational domain through line integrals over the approximation of the gradient of the velocity and a suitable decomposition of the pressure in the computational domain is employed to obtain an approximation of the pressure having zero-mean in the domain . Under assumptions related to the distance between the computational boundary and the boundary of Ω , we provide stability estimates of the solution that will lead us to the well-posedness of the scheme and also to the error estimates. In particular, we prove that the approximations of the pressure, velocity and its gradient are of order h^k+1, where h is the meshsize and k the polynomial degree of the local discrete spaces. We provide numerical experiments validating the theory and also showing the performance of the method when applied to the steady-state incompressible Navier- Stokes equations.