Anisotropic finite elements with high aspect ratio for an Asymptotic Preserving method for highly anisotropic elliptic equation
This work improves computational efficiency for solving highly anisotropic elliptic equations, which are important in plasma physics and other domains, by enabling accurate solutions with fewer mesh points.
The authors generalize an asymptotic-preserving method for highly anisotropic elliptic equations by adding a stabilization term, and propose anisotropic error indicators with mesh adaptation that reduce mesh points while achieving high precision, with meshes having aspect ratios over 500.
The concern of this work is the generalization of an Asymptotic Preserving method for the highly anisotropic elliptic equations presented in [P. Degond, A. Lozinski, J. Narski, and C. Negulescu. An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition. J. Comput. Phys., 231(7):2724{2740, 2012]. The limitations of the method introduced there in are omitted by the introduction of a stabilization term in the Asymptotic Reformulation. Furthermore, anisotropic error indicators and mesh adaptation algorithms are proposed and tested allowing to reduce considerably the number of mesh points required to achieve prescribed precision. Reported meshes have maximum aspect ratio greater than 500.