We present here different situations in which the filtering of high or low modes is used either for stabilizing semi-implicit numerical schemes when solving nonlinear parabolic equations, or for building adapted damping operators in the case of dispersive equation. We consider numerical filtering provided by mutigrid-like techniques as well as the filtering resulting from operator with monotone symbols. Our approach applies to several discretization techniques and we focus on finite elements and finite differences. Numerical illustrations are given on Cahn-Hilliard, Korteweig-de Vries and Kuramoto-Sivashinsky equations.

中文翻译：

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用于时间相关 PDE 建模和仿真的阻尼、稳定和数值滤波

我们在这里介绍了不同的情况，其中高或低模式的过滤用于在求解非线性抛物线方程时稳定半隐式数值方案，或在色散方程的情况下用于构建自适应阻尼算子。我们考虑由类似多网格的技术提供的数值过滤以及由具有单调符号的算子产生的过滤。我们的方法适用于几种离散化技术，我们专注于有限元和有限差分。给出了 Cahn-Hilliard、Korteweig-de Vries 和 Kuramoto-Sivashinsky 方程的数值说明。