On the Behavior of Two C1 Finite Elements Versus Anisotropic Diffusion

Heat transfer in magnetically confined plasmas is characterized by extremely high anisotropic diffusion phenomena. At the core of a magnetized plasma, the heat conductivity coefficients in the parallel and perpendicular directions of the induction field can be very different. Their ratio can exceed , and the pollution by purely numerical errors can make the simulation of the heat transport in the perpendicular direction very difficult. Standard numerical methods, generally used in the discretization of classical diffusion problems, are rather inefficient. The present paper analyzes a finite element approach for the solution of a highly anisotropic diffusion equation. Two families of finite elements of class , namely bi‐cubic Hermite‐Bézier and reduced cubic Hsieh‐Clough‐Tocher finite elements, are compared. Their performances are tested numerically for various ratios of the diffusion coefficients, on different mesh configurations, even aligned with the induction field. The time stepping is realized by an implicit high‐order Gear finite difference scheme. An example of a reduced model is also provided to comment on some obtained results.