论文标题
抛物线寄生虫$ P $ -LAPLACE方程的有限差异方案
Finite difference schemes for the parabolic $p$-Laplace equation
论文作者
论文摘要
我们为退化抛物线方程\ [\ partial_t u- \ mbox {div}（| \ nabla u |^{p-2} \ nabla u）= f，\ \ quad p \ geq 2。\]提出了一个新的有限差异方案。稳定性类型CFL条件。我们方法的一个重要优点是，CFL条件利用了计划降低计算成本的规律性。特别是，对于Lipschitz的数据，CFL条件的顺序与热方程式相同，独立于$ p $。
We propose a new finite difference scheme for the degenerate parabolic equation \[ \partial_t u - \mbox{div}(|\nabla u|^{p-2}\nabla u) =f, \quad p\geq 2. \] Under the assumption that the data is Hölder continuous, we establish the convergence of the explicit-in-time scheme for the Cauchy problem provided a suitable stability type CFL-condition. An important advantage of our approach, is that the CFL-condition makes use of the regularity provided by the scheme to reduce the computational cost. In particular, for Lipschitz data, the CFL-condition is of the same order as for the heat equation and independent of $p$.
