A stabilized extremum-preserving scheme for nonlinear parabolic equation on polygonal meshes

In this paper, a stabilized extremum-preserving scheme is introduced for the nonlinear parabolic equation on polygonal meshes. The so-called harmonic averaging points located at the interface of heterogeneity are employed to define the auxiliary unknowns and can be interpolated by the cell-centered unknowns. This scheme has only cell-centered unknowns and possesses a small stencil. A stabilized term is constructed to improve the stability of this scheme. The stability analysis of this scheme is obtained under standard assumptions. Numerical results illustrate that the scheme satisfies the extremum principle with anisotropic full tensor coefficient problems and has optimal convergence rate in space on distorted meshes.