A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems
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We present a technique to correct the cell-centered finite element scheme  (FECC) for full anisotropic diffusion problems on general meshes, which provides a discrete maximum principle (DMP). The correction scheme, named monotone nonlinear cell centered finite element scheme (MNFECC), is cell-centered in the sense that the solution can be computed from cell unknowns of the general primal mesh. Moreover, its coercivity and convergence are proven in a rigorous theoretical framework. Numerical experiments show that the method is effective and accurate, and it satisfies the discrete maximum principle.
CitationDao, N. A., Vo, D. C. H., & Ong, T. H. (2019). A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems. Electronic Journal of Differential Equations, 2019(122), pp. 1-23.
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