Vertex-centered linearity-preserving schemes for nonlinear parabolic problems on polygonal grids
A family of vertex-centered finite volume schemes is constructed for the numerical solution of highly nonlinear parabolic equations with applications to radiation hydrodynamics and magneto hydrodynamics. The primary unknowns are defined at the cell vertices and the derivation of the scheme is performed through a linearity preserving approach. The scheme is locally conservative, linearity preserving, coercive on arbitrary polygonal grids with star shaped cells and capable of handling arbitrary discontinuities. Examples are demonstrated on elliptic problems with discontinuities, nonlinear parabolic problem, radiation diffusion problem and spherical nonlinear heat wave; it is shown that the scheme can work well although with low convergence. Several theorems and lemmas are stated and proved.
scientific article; zbMATH DE number 6849479
scientific article