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

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.