Runge-Kutta time discretization of parabolic differential equations on evolving surfaces
Runge-Kutta time discretization of parabolic differential equations on evolving surfaces
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DOI：
10.1093/imanum/drr017
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发表时间：
2012-04-01
影响因子：
2.1
通讯作者：
Mansour, D.
中科院分区：
文献类型：
--
作者：
Dziuk, G.;Lubich, Ch.;Mansour, D.
本文首先用演化曲面有限元对运动曲面上的线性抛物型微分方程进行空间离散，然后用隐式龙格-库塔（RK）法对运动曲面上的线性抛物型方程进行时间离散。对于代数稳定和刚性精确的RK方法，证明了全离散化的无条件稳定性，并分析了其收敛性。此外，实施描述的情况下，Radau IIA时间离散化。数值实验说明了行为的全离散方法。
A linear parabolic differential equation on a moving surface is first discretized in space by evolving surface finite elements and then in time by an implicit Runge-Kutta (RK) method. For algebraically stable and stiffly accurate RK methods unconditional stability of the full discretization is proven and the convergence properties are analysed. Moreover, the implementation is described for the case of the Radau IIA time discretization. Numerical experiments illustrate the behaviour of the fully discrete method.