Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes (Communications in Computational Physics, 2018)
We construct a nonlinear monotone finite volume scheme for three-dimensionaldiffusion equation on tetrahedral meshes. Since it is crucial importantto eliminate the vertex unknowns in the construction of the scheme, we present a newefficient eliminating method. The scheme has only cell-centered unknowns and candeal with discontinuous or tensor diffusion coefficient problems on distorted meshesrigorously. The numerical results illustrate that the resulting scheme can preserve positivityon distorted tetrahedral meshes, and also show that our scheme appears to beapproximate second-order accuracy for solution.