数值流形单元法数学网格自适应

基于数值流形方法和有限覆盖技术,将有限元法的后验误差估计理论及h型网格自适应技术推广应用到数值流形单元法中,提出了数值流形单元法的后验误差估计方法和数学网格自适应技术,并编制了相应的程序。数值算例表明,经过网格自适应,可以在粗糙的初始网格基础上得到质量比较理想的网格,计算结果可达到用户要求的精度。

Mathematical mesh adaptation of numerical manifold element method

A-posteriori error estimation theory and a practical and effective h-type adaptive procedure for numerical manifold element method are presented.The relative error factors of manifold element and discrete system are defined in energy norm.To estimate the relative error factors,the exact stresses are approximately determined through stresses on Gaussian points basing on the numerical manifold method and finite cover technology.All manifold elements with relative error factor determined to exceed a pre-assigned limit are automatically refined until the relative error factor of discrete system satisfies a prescribed demand.The corresponding program is coded and two examples,one is an L-shaped structure and the other is a soil slope,are analyzed.The results indicate that the procedure can give nearly optical mesh and is practical and effective for both regular problems and problems with strong singularities.