本文關(guān)鍵詞：瞬態(tài)熱傳導(dǎo)問題的插值型無單元伽遼金方法及誤差分析　出處：《太原科技大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 插值移動(dòng)最小二乘法 形函數(shù) 插值型無單元Galerkin方法 誤差估計(jì) 瞬態(tài)熱傳導(dǎo)問題

【摘要】：本文主要使用無網(wǎng)格方法中的插值型無單元Galerkin方法。在插值型無單元Galerkin方法中,利用插值移動(dòng)最小二乘法得到形函數(shù),用Galerkin積分弱形式離散微分方程。首先討論插值移動(dòng)最小二乘法及其誤差分析理論。其次利用插值移動(dòng)最小二乘法建立形函數(shù),結(jié)合瞬態(tài)熱傳導(dǎo)的Galerkin積分弱形式,提出求瞬態(tài)熱傳導(dǎo)問題數(shù)值解的插值型無單元Galerkin方法,并推導(dǎo)出瞬態(tài)熱傳導(dǎo)問題的誤差估計(jì)式。用兩個(gè)數(shù)值算例驗(yàn)證該方法,得出兩種類型誤差范數(shù)的收斂速度是一致的。最后利用插值移動(dòng)最小二乘法建立形函數(shù),結(jié)合廣義Fisher方程的Galerkin積分弱形式,提出求廣義Fisher方程數(shù)值解的插值型無單元Galerkin方法,該方法在求解偏微分方程定解問題時(shí)可以直接施加本質(zhì)邊界條件,提高了求解效率。并給出相應(yīng)的數(shù)值算例進(jìn)行驗(yàn)證。
[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.
【學(xué)位授予單位】：太原科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.8

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