求解渗流自由面的有限元混合不动点法

基于有自由面渗流分析的高斯点,建立了求解渗流问题的非光滑非线性方程组模型和求解此类问题的有限元混合不动点算法,此方法属于固定网格法,只需划分一次网格,不需要对数据做任何近似处理,完全利用程序迭代计算渗流自由面.讨论了非光滑方程组解的存在性和该不动点算法的收敛性,通过节点压强插值绘制出渗流自由面.算例结果表明,该方法简单且收敛速度快.对不动点法的收敛性分析为迭代法的收敛提供了理论依据.

Mixed fixed-point FE method for seepage problems with free surfaces

Based on the Gauss point method for nonlinear equations model for seepage problem is seepage problem with free surface, the non-smooth proposed. At the same time, the mixed fixed-point finite element method is also presented, in which the finite element mesh is fixed. Only once grid mesh is needed and no approximate treatment of calculation data is needed by this method. The free surface can be calculated precisely through program iteration. The existence of the solution of non-smooth equations and the convergence of the proposed fixed-point method are discussed. Moreover, the free surface of seepage is plotted through interpolation of pressure intensity on the nodes. Numerical results show that the new method is simple and possesses rapid convergence rate. It also offers a theoretical basis for convergence analysis of iterative method.