Error Estimates for Advanced Galerkin Methods
暫譯: 高級Galerkin方法的誤差估計
Ruter, Marcus Olavi
- 出版商: Springer
- 出版日期: 2019-11-08
- 售價: $6,780
- 貴賓價: 9.5 折 $6,441
- 語言: 英文
- 頁數: 508
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3030061728
- ISBN-13: 9783030061722
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商品描述
This monograph provides a compendium of established and novel error estimation procedures applied in the field of computational mechanics. It also includes details of their derivations to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, the book focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, the book is intended for students, researchers and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.
商品描述(中文翻譯)
本專著提供了在計算力學領域中應用的既有及新穎誤差估計程序的彙編。它還包括這些程序的推導細節,以提供對於控制使用Galerkin方法在有限及線性化超彈性中所獲得誤差的概念的深入了解。所介紹的Galerkin方法被視為先進方法,因為它們彌補了傳統有限元素法的某些不足,後者是典型的Galerkin(基於網格)方法。特別地,本書專注於系統性推導用於構建Galerkin基於網格和無網格方法的形狀函數。考慮的基於網格的方法包括(傳統的)位移基礎、(對偶)混合、平滑及擴展有限元素法。此外,它還介紹了無元素Galerkin法和重現核粒子法,作為一類Galerkin無網格方法的代表。書中包括與工程相關的插圖數值範例,特別強調彈性斷裂力學問題,旨在幫助學生、研究人員和實務工作者提高其數值模擬的可靠性,並希望更好地掌握Galerkin方法及相關誤差估計程序的概念。