In this work, we carry out the convergence analysis of a positive DDFV method for approximating solutions of degenerate parabolic equations. The basic idea rests upon different approximations of the fluxes on the same interface of the control volume. Precisely, the approximated flux is split into two terms corresponding to the primal and dual normal components. Then the first term is discretized using a centered scheme whereas the second one is approximated in a non evident way by an upstream scheme. The novelty of our approach is twofold: on the one hand we prove that the resulting scheme preserves the positivity and on the other hand we establish energy estimates. Some numerical tests are presented and they show that the scheme in question turns out to be robust and efficient. The accuracy is almost of second order on general meshes when the solution is smooth.

中文翻译：

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退化抛物方程的正非线性DDFV格式的收敛性

在这项工作中，我们进行了正DDFV方法的收敛性分析，以近似退化的抛物方程的解。基本思想基于控制体积相同界面上通量的不同近似值。精确地，将近似通量分为对应于原始分量和对偶正态分量的两个项。然后，第一项使用居中方案离散化，而第二项通过上游方案以不明显的方式近似。我们方法的新颖性是双重的：一方面，我们证明所产生的方案保留了积极性，另一方面，我们建立了能量估计。进行了一些数值测试，结果表明所讨论的方案是可靠且有效的。