一类陆地冰川动力学模型的有限元格式 Alternative Title Finite Element Scheme of the Dynamics Model for a Class of Terrestrial Glaciers 段小丽 Thesis Advisor 周宇斌 2015-05-31 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 有限元法 变分形式 有限元格式 冰川动力学模型 Stokes 方程 Abstract 有限元法是一种高效能且比较常用的数值方法, 它被广泛应用于求解各类偏微分方程中. 本文对于一类陆地冰川动力学模型 ( 封闭的热力Stokes 方程组 ) 和三维定常 Stokes 方程运用有限元法, 得到其有限元格式, 并运用数值实验说明该方法的可行性和有效性.对于陆地冰川动力学模型, 本文对其空间变量进行有限元离散, 对时间变量进行有限差分离散, 对于非线性项采用系数有限元法离散, 最终得到其有限元格式. 其中, 在一维情形下讨论了方程的存在唯一性, 并在两个数值例子中应用此方法, 对于最终的非线性方程组, 本文采用 Newton 迭代法.对于三维 Stokes 方程, 本文对其区域进行四面体剖分和立方体剖分, 以其剖分内点为考虑对象, 计算得到在这两种剖分下的离散格式, 并通过数值实验说明其方法的有效性和可行性. Other Abstract Finite Element Method is a highly efficient and relatively common numerical method,which is widely used to solve all kinds of partial differential equations.In this paper,this glaciers dynamics model (closed thermodynamic Stokes equations) and three-dimensional Stokes equations used Finite Element Method,get its finite element formats.By using two examples to illustrate the feasibility and effectiveness of this method.For this glacier dynamics model,this paper acted finite element discrete for the spatial variables,finite-difference discrete for the time variables and the coefficient finite element discrete for the nonlinear terms,finally get its finite element format.In addition, this paper discussed the existence and uniqueness of this model in one-dimensional case.This finite element format was used in two examples, we used the Newton iterative method for the final nonlinear equations.For the three-dimensional Stokes equations, the paper conducted the tetrahedron split and the cube split for its region,get two the discrete format.using this discrete format for these equations,and you can see its effectiveness and feasibility through numerical experiments. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224473 Collection 数学与统计学院 Recommended CitationGB/T 7714 段小丽. 一类陆地冰川动力学模型的有限元格式[D]. 兰州. 兰州大学,2015.
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