In this paper, we develop an oscillation free local discontinuous Galerkin (OFLDG) method for solving nonlinear degenerate parabolic equations. Following the idea of our recent work [J. Lu, Y. Liu, and C.-W. Shu, SIAM J. Numer. Anal. 59(2021), pp. 1299-1324.], we add the damping terms to the LDG scheme to control the spurious oscillations when solutions have a large gradient. The $L^2$-stability and optimal priori error estimates for the semi-discrete scheme are established. The numerical experiments demonstrate that the proposed method maintains the high-order accuracy and controls the spurious oscillations well.

中文翻译：

---

非线性退化抛物线方程的一种无振荡局部不连续伽辽金方法

在本文中，我们开发了一种用于求解非线性退化抛物线方程的无振荡局部不连续伽辽金 (OFLDG) 方法。遵循我们最近工作的想法 [J. Lu、Y. Liu 和 C.-W. Shu, SIAM J. 数字。肛门。59(2021), pp. 1299-1324.]，我们将阻尼项添加到 LDG 方案中，以在解具有大梯度时控制虚假振荡。建立了半离散方案的$L^2$-稳定性和最优先验误差估计。数值实验表明，所提出的方法保持了高阶精度，并能很好地控制杂散振荡。