Abstract
When the eigenvalue problem of the linearized magnetohydrodynamics equation is solved by finite-element methods, whether energy integrals are exactly carried out or not affects the convergence properties of eigenvalues. If the energy integrals are exactly carried out, the eigenvalue of the most violent instability (the lowest eigenvalue) is approximated from “above, ” that is, the approximated eigenvalue decreases towards the true eigenvalue as the number of elements increases. If the energy integrals are estimated by Gaussian quadrature formulas in which errors are of the same order as those by the finite-element method, the lowest eigenvalue is approximated from “below.”
