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內容簡介

　　有限元方法是現代科學與工程計算領域中最廣泛使用的數值方法之一, 間斷有限元方法則是傳統（連續）有限元方法的創新形式、改進和發展。《信息與計算科學叢書：間斷有限元理論與方法（修訂版）》係統地闡述間斷有限元基本理論、思想和方法。
　　《信息與計算科學叢書：間斷有限元理論與方法（修訂版）》主要針對橢圓方程、一階雙麯方程、一階正對稱雙麯方程組、對流擴散方程、Stokes 方程和橢圓變分不等式等偏微分方程定解問題, 介紹各種形式間斷有限元方法的構造、穩定性和誤差分析、超收斂性質、後處理技術、後驗誤差估計和自適應計算。

目錄

第1章 預備知識
1.1 Sobolev空間簡介
1.2 嵌入越
1.3 有限元空間及其性質
1.3.1 有限元空間
1.3.2 插值和投影逼近
1.3.3 逆性質和跡不等式
1.4 橢圓邊值問題的有限元方法
1.4.1 邊值問題的適定性
1.4.2 連續有限元逼近

第2章 橢圓問題懲罰形式的間斷有限元方法
2.1 曆史的迴顧
2.2 懲罰方法的一般理論
2.3 相容方法
2.4 不相容方法
2.5 離散方程組的條件數
2.6 後驗誤差分析
2.6.1 後驗誤差上界估計
2.6.2 後驗誤差下界估計
2.6.3 數值算法
2.7 插值函數的超逼近性質
2.7.1 一維插值函數的超逼近性質
2.7.2 高維插值函數的超逼近性質
2.8 後處理技術與超收斂性
2.8.1 超逼近估計
2.8.2 i2-投影的後處理技術
2.8.3 導數小片插值恢復技術
2.8.4 整體插值後處理技術

第3章 橢圓相關問題的間斷有限元方法
3.1 對流占優反應擴散方程
3.1.1 間斷有限元格式
3.1.2 穩定性與誤差分析
3.1.3 超收斂與後驗誤差估計
3.2 Stokes問題
3.2.1 綫性速度-常數壓力間斷元
3.2.2 誤差分析
3.2.3 高次間斷有限元
3.3 橢圓變分不等式問題
3.3.1 問題及其間斷有限元近似
3.3.2 最優誤差估計與迭代求解
3.4 第二類橢圓變分不等式
3.4.1 問題及其正則化
3.4.2 間斷有限元方法
3.4.3 先驗誤差估計
3.4.4 後驗誤差估計
3.4.5 數值計算例

第4章 數值通量形式的間斷有限元方法
4.1 介紹
4.2 數值通量方法的基本公式
4.3 基本公式的理論分析
4.4 不穩定格式
4.5 廣義局部間斷有限元方法
4.6 對流擴散問題
4.6.1 迎風型間斷有限元格式
4.6.2 誤差分析
4.6.3 對流擴散反應方程
4.7 橢圓相關問題

第5章 一階雙麯方程的間斷有限元方法
5.1 起源與曆史發展
5.2 問題及其間斷有限元格式
5.3 最優階誤差估計
5.4 三角元的超收斂估計
5.5 矩形元的超收斂估計
5.5.1 對流方嚮平行坐標軸情形
5.5.2 一般情形的矩形元
5.6 有關近似的超收斂估計
5.6.1 對流方嚮導數的後處理
5.6.2 負範數誤差估計與均值逼近
5.6.3 數值計算例
5.7 後驗誤差分析
5.7.1 後驗誤差估計：特殊網格情形
5.7.2 後驗誤差估計：一般網格情形
5.7.3 後驗誤差下界估計
5.7.4 數值計算例
5.8 非定常問題
5.8.1 半離散間斷有限元逼近
5.8.2 全離散間斷有限元逼近
5.8.3 後驗誤差分析

第6章 一階正對稱雙麯方程組的間斷有限元方法
6.1 -階正對稱_方程組
6.2 擬迎風間斷有限元方法
6.2.1 擬迎風格式及其穩定性
6.2.2 最優階誤差估計
6.2.3 負範數誤差估計
6.2.4 數值計算例
6.3 懲罰形式的間斷有限元方法
6.4 插值函數的超逼近性質
6.4.1 強正規三角剖分
6.4.2 幾乎一緻的矩形剖分
6.5 懲罰方法的超收斂估計
6.5.1 綫性三角元
6.5.2 雙綫性矩形元
6.6 非定常問題
6.6.1 半離散間斷有限元近似
6.6.2 全離散間斷有限元近似
6.7 顯式時空間斷有限元方法
6.7.1 時空間斷有限元格式及其穩定性
6.7.2 誤差分析
6.8 半顯式時空間斷有限元格式
6.8.1 半顯式格式
6.8.2 誤差分析
參考文獻
索引
《信息與計算科學叢書》已齣版書目

前言/序言

信息與計算科學叢書：間斷有限元理論與方法（修訂版） 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

The subtitle, Nonclassical Fields, is perhaps not as accurate as it might be as a summary of content; or to put it another way, if my aim from the start had been to write a book on this topic, parts of that book would differ significantly from what follows here. Possibly the most important thing missing, and something that should be said, is that there are two quite distinct paths to a definition of nonclassicality in quantum optics. The first is grounded in the existence, or otherwise, of a nonsingular and positrve Glauber-Sudarshan P function. The physical grounding is in the treatment of optical measurements, specifically the photoelectric effect: for a given optical field, can the photoelectron counting statistics, including all correlations, be reproduced by a Poisson process of photoelectron generation driven by a classicallight intensity, allowed most generally to be stochastic? Viewed at a more informallevel, the question asks whether or not the infamous proposal of Bohr, Kramers, and Slater for the interaction of classical light and quantized atoms can be upheld in the presence of the observable photoelectron counting statistics.

評分☆☆☆☆☆

需要較好的數學功底，隻是想編程的，這本書不適閤。

評分☆☆☆☆☆

需要較好的數學功底，隻是想編程的，這本書不適閤。

評分☆☆☆☆☆

需要較好的數學功底，隻是想編程的，這本書不適閤。

評分☆☆☆☆☆

The subtitle, Nonclassical Fields, is perhaps not as accurate as it might be as a summary of content; or to put it another way, if my aim from the start had been to write a book on this topic, parts of that book would differ significantly from what follows here. Possibly the most important thing missing, and something that should be said, is that there are two quite distinct paths to a definition of nonclassicality in quantum optics. The first is grounded in the existence, or otherwise, of a nonsingular and positrve Glauber-Sudarshan P function. The physical grounding is in the treatment of optical measurements, specifically the photoelectric effect: for a given optical field, can the photoelectron counting statistics, including all correlations, be reproduced by a Poisson process of photoelectron generation driven by a classicallight intensity, allowed most generally to be stochastic? Viewed at a more informallevel, the question asks whether or not the infamous proposal of Bohr, Kramers, and Slater for the interaction of classical light and quantized atoms can be upheld in the presence of the observable photoelectron counting statistics.

評分☆☆☆☆☆

The subtitle, Nonclassical Fields, is perhaps not as accurate as it might be as a summary of content; or to put it another way, if my aim from the start had been to write a book on this topic, parts of that book would differ significantly from what follows here. Possibly the most important thing missing, and something that should be said, is that there are two quite distinct paths to a definition of nonclassicality in quantum optics. The first is grounded in the existence, or otherwise, of a nonsingular and positrve Glauber-Sudarshan P function. The physical grounding is in the treatment of optical measurements, specifically the photoelectric effect: for a given optical field, can the photoelectron counting statistics, including all correlations, be reproduced by a Poisson process of photoelectron generation driven by a classicallight intensity, allowed most generally to be stochastic? Viewed at a more informallevel, the question asks whether or not the infamous proposal of Bohr, Kramers, and Slater for the interaction of classical light and quantized atoms can be upheld in the presence of the observable photoelectron counting statistics.

評分☆☆☆☆☆

需要較好的數學功底，隻是想編程的，這本書不適閤。

評分☆☆☆☆☆

需要較好的數學功底，隻是想編程的，這本書不適閤。

評分☆☆☆☆☆

需要較好的數學功底，隻是想編程的，這本書不適閤。

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