On a Computational Advantageous Voigt Regularization for Geophysical Flows

Abstract

In this paper we study a linearized Crank-Nicolson in time and Finite Element in space algorithm for the BV-Voigt regularization model of geophysical flows, which presents interesting advantages from the computational point of view. We prove the algorithm conserves energy and is unconditionally stable and optimally convergent. Lastly, we show that the BV-Voigt model provides accurate solutions and compares favorably with a related regularization model in a coarse mesh, a case in which the BV model solution degenerates.