Analysis of some moving space-time finite element methods
Analysis of some moving space-time finite element methods
复制标题
DOI：
10.1137/0730001
复制
发表时间：
1993-02
影响因子：
2.9
通讯作者：
R. Bank;R. Santos
中科院分区：
文献类型：
--
作者：
R. Bank;R. Santos
定义并分析了求解含时偏微分方程组的两种时空有限元方法。该方法基于等参数有限元隐式定义运动网格在空间维度上的时间离散。一种方法允许以连续方式添加和删除节点，而另一种方法允许在网格中进行不连续的更改(静态重分区)。对一个可能含有大对流项的抛物型方程模型进行了详细的收敛分析。在这里，作者得到了对称的最佳逼近误差估计，类似于Dupont[Math.Comp.，39(1982)，pp.85-107]对于半离散情况。
Two space-time finite element methods for solving time-dependent partial differential equations are defined and analyzed. The methods are based on the use of isoparametric finite elements to implicitly define the time discretization on a moving mesh in the space dimensions. One method allows for adding and deleting knots in a continuous fashion, while the other allows for discontinuous changes in the mesh (static rezone). A detailed convergence analysis for a model parabolic equation, with a possibly large convection term is presented. Here the authors obtain symmetric best approximation error estimates similar to those obtained by Dupont [Math. Comp., 39 (1982), pp. 85–107] for the semidiscrete case.