Adaptive finite elements for a set of second-order ODEs

Abstract

A Hermite finite-elements approach with adaptive mesh refinement for the solution of a set of second-order ordinary differential equations is described. The main advantage of the method is its usability for stiff equations with boundary conditions. For cases where exponentially growing solutions can exist, the method overcomes the common problems of initial value solvers. The method was successfully used for the full-wave solution of wave propagation in inhomogeneous plasma where the mode conversion process between ordinary, extraordinary and electron Bernstein waves occurs.