Dao, Nguyen AnhVo, Duc Cam HaiOng, Thanh Hai2021-12-062021-12-062019-11-19Dao, N. A., Vo, D. C. H., & Ong, T. H. (2019). A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems. <i>Electronic Journal of Differential Equations, 2019</i>(122), pp. 1-23.1072-6691https://hdl.handle.net/10877/15016We present a technique to correct the cell-centered finite element scheme [20] (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.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalDiscrete maximum principleHeterogeneous anisotropic diffusionGeneral gridFinite volumeFinite elementsCell-centered schemeArticle