Duality-based asymptotic-preserving method for highly anisotropic diffusion equations (Q357486)

The authors introduce an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic preserving reformulation of the original system, permitting an accurate resolution independently of the anisotropy strength and without the need of a mesh adapted to this anisotropy. The counterpart of this procedure is the larger system size, enlarged by adding auxiliary variables and Lagrange multipliers. This asymptotic-preserving method generalizes the method provided in the work by \textit{P. Degond}, \textit{F. Deluzet} and \textit{C. Negulescu} [Multiscale Model. Simul. 8(2009), No. 2, 645--666 (2010; Zbl 1190.35216)] to the case of an arbitrary anisotropy direction field.