Communications in Mathematical Sciences
Volume 10 (2012)
Special Issue on the Occasion of C. David Levermore’s Sixtieth Birthday
Duality-based asymptotic-preserving method for highly anisotropic diffusion equations
Pages: 1 – 31
The present paper introduces 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 original procedure is the larger system size, enlarged by adding auxiliary variables and Lagrange multipliers. This Asymptotic-Preserving method generalizes the method investigated in a previous paper [P. Degond, F. Deluzet, and C. Negulescu, Multiscale Model. Simul., 8(2), 645–666, 2009/10] to the case of an arbitrary anisotropy direction field.
anisotropic diffusion, asymptotic preserving scheme, finite element method
2010 Mathematics Subject Classification