By Dr. Ricardo Oyarzúa, profesor de la Universidad del Bío Bío, Concepción, Chile
Seminar Date: 2021-06-10
In this talk we present a new conforming mixed finite element method for the Navier-Stokes problem posed on non-standard Banach spaces, where a pseudostress tensor and the velocity are the main unknowns of the system. The associated Galerkin scheme can be defined by employing Raviart–Thomas elements of degree $k$ for the pseudostress and discontinuous piece–wise polynomials of degree $k$ for the velocity. Next, by extending standard techniques commonly used on Hilbert spaces to the case of Banach spaces, we derive a reliable and efficient residual-based a posteriori error estimator for the corresponding mixed scheme.