瞬态热传导问题的插值型无单元伽辽金方法及误差分析

发布时间：2018-01-08 02:09

本文关键词：瞬态热传导问题的插值型无单元伽辽金方法及误差分析　出处：《太原科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文主要使用无网格方法中的插值型无单元Galerkin方法。在插值型无单元Galerkin方法中,利用插值移动最小二乘法得到形函数,用Galerkin积分弱形式离散微分方程。首先讨论插值移动最小二乘法及其误差分析理论。其次利用插值移动最小二乘法建立形函数,结合瞬态热传导的Galerkin积分弱形式,提出求瞬态热传导问题数值解的插值型无单元Galerkin方法,并推导出瞬态热传导问题的误差估计式。用两个数值算例验证该方法,得出两种类型误差范数的收敛速度是一致的。最后利用插值移动最小二乘法建立形函数,结合广义Fisher方程的Galerkin积分弱形式,提出求广义Fisher方程数值解的插值型无单元Galerkin方法,该方法在求解偏微分方程定解问题时可以直接施加本质边界条件,提高了求解效率。并给出相应的数值算例进行验证。
[Abstract]:In this paper, we mainly use the interpolating element free Galerkin method in the meshless method. In the interpolating cell-free Galerkin method, we use the interpolation moving least square method to get the shape function. In this paper, Galerkin integral weak form discrete differential equation is used. Firstly, the interpolation moving least square method and its error analysis theory are discussed. Secondly, the shape function is established by interpolation moving least square method. Combined with the weak form of Galerkin integral of transient heat conduction, an interpolated element-free Galerkin method is proposed to solve the numerical solution of transient heat conduction problem. The error estimation formula of transient heat conduction problem is derived. Two numerical examples are used to verify the method and the convergence rate of the two kinds of error norms is obtained. Finally, the shape function is established by interpolating moving least square method. Combined with the weak form of Galerkin integral of generalized Fisher equation, an interpolation-free Galerkin method for solving the numerical solution of generalized Fisher equation is proposed. This method can directly apply essential boundary conditions to solve the definite solution of partial differential equations, and improves the efficiency of the solution, and the corresponding numerical examples are given to verify the proposed method.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8

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