High-order primal mixed finite element method for boundary-value correction on curved domain

This paper addresses the non-homogeneous Neumann boundary condition on domains with curved boundaries. We consider the Raviart-Thomas element (RTk ) of degree $k\ge 1$on triangular mesh. on a triangular mesh. A key feature of our boundary value correction method is the shift from the true boundary to a surrogate boundary. We present a high-order version of the method, achieving an $O(h^k+1\mathrm{/}2)$ convergence in $L^2$-norm estimate for the velocity field and an $O(h^k)$ convergence in $H^1$-norm estimate for the pressure. Finally, numerical experiments validate our theoretical results.