Finite Element Methods in Linear Ideal Magnetohydrodynamics

Inhaltsverzeichnis

• 1. Finite Element Methods for the Discretization of Differential Eigenvalue Problems.
• 1.1 A Classical Model Problem.
• 1.2 A Non-Standard Model Problem.
• 1.3 Spectral Stability.
• 1.5 Some Comments.
• 2. The Ideal MHD Model.
• 2.1 Basic Equations.
• 2.2 Static Equilibrium.
• 2.3 Linearized MHD Equations.
• 2.4 Variational Formulation.
• 2.5 Stability Considerations.
• 2.6 Mechanical Analogon.
• 3. Cylindrical Geometry.
• 3.1 MHD Equations in Cylindrical Geometry.
• 3.2 Six Test Cases.
• 3.3 Approximations.
• 3.4 Polluting Finite Elements.
• 3.6 Non-Conforming Non-Polluting Elements.
• 3.7 Applications and Comparison Studies (with M.
• A. Secrétan).
• 3.8 Discussion and Conclusion.
• 4. Two-Dimensional Finite Elements Applied to Cylindrical Geometry.
• 4.1 Conforming Finite Elements.
• 4.2 Non-Conforming, Finite Hybrid Elements.
• 4.3 Discussion.
• 5. ERATO: Application to Toroidal Geometry.
• 5.1 Static Equilibrium.
• 5.2 Mapping of (?, ?) into (?, ?) Coordinates in ? p.
• 5.3 Variational Formulation of the Potential and Kinetic Energies..
• 5.4 Variational Formulation of the Vacuum Energy.
• 5.5 Finite Hybrid Elements.
• 5.6 Extraction of the Rapid Angular Variation.
• 5.7 Calculation of ?-Limits (with F. Troyon).
• 6. HERA: Application to Helical Geometry (Peter Merkel, IPP Garching).
• 6.1 Equilibrium.
• 6.2 Variational Formulation of the Stability Problem.
• 6.3 Applications.
• 7. Similar Problems.
• 7.1 Similar Problems in Plasma Physics.
• 7.2 Similar Problems in Other Domains.
• Appendices.
• A: Variational Formulation of the Ballooning Mode Criterion.
• B.1 The Problem.
• B.2 Two Numberings of the Components.
• B.3 Resolution for Numbering (D1).
• B.4 Resolution for Numbering (D2).
• B.5 Higher Order Finite Elements.
• C: Organization of ERATO.
• D: Listing of ERATO 3 (with R. Iacono).
• References.