TY - JOUR
T1 - Numerical Analysis of a Finite Element Crank-Nicolson Discretization for MHD Flows at Small Magnetic Reynolds Numbers
AU - G. Yuksel & R. Ingram
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 74
EP - 98
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/559.html
KW - Navier-Stokes, MHD, finite element, Crank-Nicolson.
AB - <p style="text-align: justify;">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.</p>