We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of the generating curves of the axisymmetric surfaces. The proposed numerical methods are based on piecewise linear parametric finite elements. The constructed fully practical schemes satisfy the conservation of the enclosed volume. In addition, we prove the unconditional stability and consider the distribution of vertices for the discretized schemes. The introduced methods are implicit and the resulting nonlinear systems of equations can be solved very efficiently and accurately via the Newton's iterative method. Numerical results are presented to show the accuracy and efficiency of the introduced schemes for computing the considered axisymmetric geometric flows.
翻译:我们提出并分析用于表面扩散、节制平均曲率流和轴线设置的中间进化法的体积保留参数参数参数方法; 以轴线表面的生成曲线表示薄弱的配方; 拟议的数字方法以小片线性参数限制要素为基础; 构建的完全实用的保质计划满足了封闭体积的保存; 此外, 我们证明无条件的稳定性,并考虑分解法的脊椎分布; 引入的方法是隐含的, 由此产生的非线性方程系统可以通过牛顿的迭接法非常高效和准确地解决。 数字结果显示为计算考虑的轴线性几何流而采用的办法的准确性和效率。