Abstract
In this paper, we study an efficient numerical scheme for a strongly anisotropic elliptic problem which arises, for example, in the modeling of magnetized plasma dynamics. A small parameter ? induces the anisotropy of the problem and leads to severe numerical difficulties if the problem is solved with standard methods for the case 0<??1. An Asymptotic-Preserving scheme is therefore introduced in this paper in a 2D framework, with an anisotropy aligned to one coordinate axis and an ?-intensity which can be either constant or variable within the simulation domain. This AP scheme is uniformly precise in ?, permitting thus the choice of coarse discretization grids, independent of the magnitude of the parameter ?.
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