The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle (Communications in Computational Physics, 2023)
In this paper, we correct the finite volume element methods for diffusionequations on general triangular and quadrilateral meshes. First, we decompose thenumerical fluxes of original schemes into two parts, i.e., the principal part with a two-point flux structure and the defective part. And then with the help of local extremums,we transform the original numerical fluxes into nonlinear numerical fluxes, which canbe expressed as a nonlinear combination of two-point fluxes. It is proved that thecorrected schemes satisfy the discrete strong extremum principle without restrictionson the diffusion coefficient and meshes. Numerical results indicate that the correctedschemes not only satisfy the discrete strong extremum principle but also preserve theconvergence order of the original finite volume element methods.