Beyond the Analytic Solution Manufacturing for Anisotropic Elliptic Equations

Abstract.

This article is aimed at introducing a new procedure for defining reference solutions to which the numerical approximations of anisotropic problems arising in plasma physics may be compared. In this context, the main issue is related to the construction of functions with no gradients along the vector field defining the anisotropy direction. The so-called solution manufacturing, as implemented so far in the literature, only applies to frameworks where all the computations can be carried out analytically. In the present paper, we propose a new method in which this requirement is not mandatory. Indeed, via a Riemannian metric, we use a propagation of the boundary value by the flows related to the vector field defining the anisotropy direction. This permits one to extend the application of the solution manufacturing to a broader range of contexts.