Higher order finite difference schemes for the magnetic induction   equations
  We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the stability as well as high order of accuracy of the schemes. 
Ujjwal Koley, Siddhartha Mishra, Nils Henrik Risebro, Magnus Sv\"ard
math.AP