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内容简介

　　有限元方法是现代科学与工程计算领域中最广泛使用的数值方法之一, 间断有限元方法则是传统（连续）有限元方法的创新形式、改进和发展。《信息与计算科学丛书：间断有限元理论与方法（修订版）》系统地阐述间断有限元基本理论、思想和方法。
　　《信息与计算科学丛书：间断有限元理论与方法（修订版）》主要针对椭圆方程、一阶双曲方程、一阶正对称双曲方程组、对流扩散方程、Stokes 方程和椭圆变分不等式等偏微分方程定解问题, 介绍各种形式间断有限元方法的构造、稳定性和误差分析、超收敛性质、后处理技术、后验误差估计和自适应计算。

目录

第1章 预备知识
1.1 Sobolev空间简介
1.2 嵌入越
1.3 有限元空间及其性质
1.3.1 有限元空间
1.3.2 插值和投影逼近
1.3.3 逆性质和迹不等式
1.4 椭圆边值问题的有限元方法
1.4.1 边值问题的适定性
1.4.2 连续有限元逼近

第2章 椭圆问题惩罚形式的间断有限元方法
2.1 历史的回顾
2.2 惩罚方法的一般理论
2.3 相容方法
2.4 不相容方法
2.5 离散方程组的条件数
2.6 后验误差分析
2.6.1 后验误差上界估计
2.6.2 后验误差下界估计
2.6.3 数值算法
2.7 插值函数的超逼近性质
2.7.1 一维插值函数的超逼近性质
2.7.2 高维插值函数的超逼近性质
2.8 后处理技术与超收敛性
2.8.1 超逼近估计
2.8.2 i2-投影的后处理技术
2.8.3 导数小片插值恢复技术
2.8.4 整体插值后处理技术

第3章 椭圆相关问题的间断有限元方法
3.1 对流占优反应扩散方程
3.1.1 间断有限元格式
3.1.2 稳定性与误差分析
3.1.3 超收敛与后验误差估计
3.2 Stokes问题
3.2.1 线性速度-常数压力间断元
3.2.2 误差分析
3.2.3 高次间断有限元
3.3 椭圆变分不等式问题
3.3.1 问题及其间断有限元近似
3.3.2 最优误差估计与迭代求解
3.4 第二类椭圆变分不等式
3.4.1 问题及其正则化
3.4.2 间断有限元方法
3.4.3 先验误差估计
3.4.4 后验误差估计
3.4.5 数值计算例

第4章 数值通量形式的间断有限元方法
4.1 介绍
4.2 数值通量方法的基本公式
4.3 基本公式的理论分析
4.4 不稳定格式
4.5 广义局部间断有限元方法
4.6 对流扩散问题
4.6.1 迎风型间断有限元格式
4.6.2 误差分析
4.6.3 对流扩散反应方程
4.7 椭圆相关问题

第5章 一阶双曲方程的间断有限元方法
5.1 起源与历史发展
5.2 问题及其间断有限元格式
5.3 最优阶误差估计
5.4 三角元的超收敛估计
5.5 矩形元的超收敛估计
5.5.1 对流方向平行坐标轴情形
5.5.2 一般情形的矩形元
5.6 有关近似的超收敛估计
5.6.1 对流方向导数的后处理
5.6.2 负范数误差估计与均值逼近
5.6.3 数值计算例
5.7 后验误差分析
5.7.1 后验误差估计：特殊网格情形
5.7.2 后验误差估计：一般网格情形
5.7.3 后验误差下界估计
5.7.4 数值计算例
5.8 非定常问题
5.8.1 半离散间断有限元逼近
5.8.2 全离散间断有限元逼近
5.8.3 后验误差分析

第6章 一阶正对称双曲方程组的间断有限元方法
6.1 -阶正对称_方程组
6.2 拟迎风间断有限元方法
6.2.1 拟迎风格式及其稳定性
6.2.2 最优阶误差估计
6.2.3 负范数误差估计
6.2.4 数值计算例
6.3 惩罚形式的间断有限元方法
6.4 插值函数的超逼近性质
6.4.1 强正规三角剖分
6.4.2 几乎一致的矩形剖分
6.5 惩罚方法的超收敛估计
6.5.1 线性三角元
6.5.2 双线性矩形元
6.6 非定常问题
6.6.1 半离散间断有限元近似
6.6.2 全离散间断有限元近似
6.7 显式时空间断有限元方法
6.7.1 时空间断有限元格式及其稳定性
6.7.2 误差分析
6.8 半显式时空间断有限元格式
6.8.1 半显式格式
6.8.2 误差分析
参考文献
索引
《信息与计算科学丛书》已出版书目

前言/序言

信息与计算科学丛书：间断有限元理论与方法（修订版） 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

需要较好的数学功底，只是想编程的，这本书不适合。

评分☆☆☆☆☆

需要较好的数学功底，只是想编程的，这本书不适合。

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

需要较好的数学功底，只是想编程的，这本书不适合。

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

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.

评分☆☆☆☆☆

需要较好的数学功底，只是想编程的，这本书不适合。

评分☆☆☆☆☆

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.

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