Error Estimates for Velocity-Pseudo-Stress Formulation Applied to the Generalized Oseen Problem

Abstract

[Abstract]: We consider a dual-mixed method for the generalized Oseen equations, where the velocity and pseudo-stress are treated as the primary unknowns. A stabilized discrete scheme is obtained by augmenting the dual-mixed approach with suitable least-squares terms derived from the physical equations. We prove that the scheme is well-posed using the Lax-Milgram Lemma. To approximate the unknowns, we propose using continuous piecewise polynomials for the velocity field and Raviart Thomas elements for each row of the pseudo-stress. We prove optimal a priori error estimates for this choice. We also provide a residual-based a posteriori error analysis. We derive a simple a posteriori error indicator and prove it is reliable and locally efficient. Finally, we supply some numerical experiments that confirm the theoretical results.