The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the $p$-Laplace operator since the latter lead to linear systems of equations in the time steps. The semi-implicit treatment of the operator requires introducing a regularization parameter that has to be suitably related to other discretization parameters. To avoid restrictive, unpractical conditions, a careful convergence analysis has to be carried out. The arguments presented in this article show that convergence holds under a moderate condition that relates the step size to the regularization parameter but which is independent of the spatial resolution.

中文翻译：

---

奇异抛物方程的全离散隐式和半隐式逼近的收敛

本文讨论了一类非线性抛物线演化问题的隐式和半隐式完全离散近似的收敛问题。这种方案在用 $p$-Laplace 算子定义的演化的数值解中很流行，因为后者导致时间步长中的线性方程组。算子的半隐式处理需要引入一个正则化参数，该参数必须与其他离散化参数适当相关。为了避免限制性的、不切实际的条件，必须进行仔细的收敛分析。本文中提出的论点表明，收敛保持在适度条件下，该条件将步长与正则化参数相关联，但与空间分辨率无关。