MHD Stability Analysis with Higher Order Spline Functions

The eigenvalue problem of the linearized magnetohydrodynamic (MHD) equation is formulated by using higher order spline functions as the base functions of Ritz-Galerkin approximation. When the displacement vector normal to the magnetic surface (in the magnetic surface) is interpolated by B-spline functions of degree p1 (degree p2) which is continuously c1-th (c2-th) differentiable on neighboring finite elements, the sufficient conditions for the good approximation is given by p1≥p2+1, c1≤c2+1, (c1≥1, p2≥c2≥0). The influence of the numerical integration upon the convergence of calculated eigenvalues is discussed.