In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are formulated in a one-dimensional setting, here we consider exclusively the two-dimensional case. We prove that the proposed schemes preserve fundamental structural properties like nonnegativity of the solution without restriction on the size of the mesh and entropy dissipation. Moreover, all the methods presented here are at least second order accurate in the transient regimes and arbitrarily high order for large times in the hypothesis in which the flux vanishes at the stationary state. Suitable numerical tests will confirm the theoretical results.

翻译：在这项工作中,我们考虑将最近提议的非线性Fokker-Planck型方程式数字保值结构扩大至非连续全面扩散基体。虽然在现有的工程中,这些计划是在一维环境中制定的,但这里我们只考虑二维情况。我们证明,拟议的计划保留了基本的结构特性,例如,解决方案的不可强化性,而没有限制网目和消化的大小。此外,这里提出的所有方法在瞬时制度中至少是第二级的精确度,在流动在静止状态消失的假设中大时任意高的顺序。可行的数字测试将证实理论结果。