Numerical Analysis of a Finite Element Crank-Nicolson Discretization for MHD Flows at Small Magnetic Reynolds Numbers

Abstract

We consider the finite element method for time dependent MHD flow at small magnetic Reynolds number. We make a second (and common) simplification in the model by assuming the time scales of the electrical and magnetic components are such that the electrical field responds instantaneously to changes in the fluid motion. This report gives a comprehensive error analysis for both the semi-discrete and a fully-discrete approximation. Finally, the effectiveness of the method is illustrated in several numerical experiments.