A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations (Communications in Computational Physics, 2020)
A monotone cell-centered finite volume scheme for diffusion equations ontetrahedral meshes is established in this paper, which deals with tensor diffusion coefficients and strong discontinuous diffusion coefficients. The first novelty here is topropose a new method of interpolating vertex unknowns (auxiliary unknowns) withcell-centered unknowns (primary unknowns), in which a sufficient condition is givento guarantee the non-negativity of vertex unknowns. The second novelty of this paperis to devise a modified Anderson acceleration, which is based on an iterative combination of vertex unknowns and will be denoted as AA-Vertex algorithm, in order to solvethe nonlinear scheme efficiently. Numerical testes indicate that our new method canobtain almost second order accuracy and is more accurate than some existing methods.Furthermore, with the same accuracy, the modified Anderson acceleration is muchmore efficient than the usual one.