Newton Type Methods for Solving Finite-ELement Space, Euler-Implicit Time Discretization of the Hasegawa-Mima Equation

Abstract

Hasegawa-Mima was derived by Akira Hasegawa and Kunioki Mima during late 70s. When normalized, it can be put as the following PDE that is third order in space and first order in time: ∆ u_t + u_t={u, ∆ u} +{p,u}

In a recent work, this equation was reformulated as a coupled system and put in variational form.

Also, a continuous Time Integral Formulation was derived over any time interval. Consequently, a finite element space semi-discretization followed by Euler-Implicit time discretization was obtained and extensively studied