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.
翻译：在本文中,我们开发了一种解决非线性退化抛物线式等式的无振动自由本地不连续加勒金(OFLDG)方法。根据我们最近工作的想法[J. Lu, Y. Liu, C.-W. Shu, SIM J. Numer. Anal. 59(2021), pp.1299-1324.],我们在LDG办法中添加了阻隔条件,以便在解决方案梯度大时控制虚假振动。确定了半分解法的可承受性和最佳先验误差估计值。数字实验表明,拟议方法保持了高端精确度,并控制了虚假振动。
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