Preprint 2025-06
Jessika Camaño, Ricardo Oyarzúa, Katherine Rojo:
A momentum and mass conservative pseudostress-based mixed finite element method for the Stokes problem
Abstract:
In this paper, we analyze a pseudostress-based mixed finite element method for the Stokes problem that ensures both mass and momentum conservation. Mass conservation is achieved by approximating the velocity using the lowest-order Raviart–Thomas elements, while momentum conservation is enforced through a discrete Helmholtz decomposition of the piecewise-constant vector space. We establish the well-posedness of the method and derive theoretical convergence rates, including a superconvergence result for the velocity gradient approximation. A key advantage of the proposed method is its computational efficiency, as it is slightly less expensive than the classical pseudostress-based approach studied in [5, 11], while also guaranteeing mass and momentum conservation. Additionally, we extend our analysis to the Stokes problem with mixed boundary conditions and present numerical experiments that confirm the theoretical results.
