Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 122, pp. 1-23.

Title: A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems

Authors: Nguyen Anh Dao (Ton Duc Thang Univ., Ho Chi Minh City, Vietnam)
                Duc Cam Hai Vo (Univ. of Science, VNU HCMC, Ho Chi Minh City, Vietnam)
               Thanh Hai Ong (Univ. of Science, VNU HCMC, Ho Chi Minh City, Vietnam)

Abstract:
 We 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.
 
Submitted July 3, 2019. Published November 19, 2019.
Math Subject Classifications:  65N08, 65N30, 65N12, 35J15.
Key Words: Discrete maximum principle; heterogeneous anisotropic diffusion;
                     general grid; finite volume; finite elements; cell-centered scheme.