Two-scale approach to oscillatory singularly perturbed transport equations. (2017)

• Record Type: Book
• Further Information: Note: Emmanuel Frénod.
• Authors: Frénod, Emmanuel
• Contents: I Two-Scale Convergence.- 1 Introduction.- 1.1 First Statements on Two-Scale Convergence.- 1.2 Two-Scale Convergence and Homogenization.- 1.2.1 How Homogenization Led to the Concept of Two-Scale Convergence.- 1.2.2 A Remark Concerning Periodicity.- 1.2.3 A Remark Concerning Weak-* Convergence.- 2 Two-Scale Convergence -- Definition and Results.- 2.1 Background Material on Two-Scale Convergence.- 2.1.1 Definitions.- 2.1.2 Link with Weak Convergence.- 2.2 Two-Scale Convergence Criteria.- 2.2.1 Injection Lemma.- 2.2.2 Two-Scale Convergence Criterion.- 2.2.3 Strong Two-Scale Convergence Criterion.- 3 Applications.- 3.1 Homogenization of ODE.- 3.1.1 Textbook Case, Setting and Asymptotic Expansion.- 3.1.2 Justification of Asymptotic Expansion Using Two-Scale Convergence.- 3.2 Homogenization of Singularly-Perturbed ODE.- 3.2.1 Equation of Interest and Setting.- 3.2.2 Asymptotic Expansion Results.- 3.2.3 Asymptotic Expansion Calculations.- 3.2.4 Justification Using Two-Scale Convergence I: Results.- 3.2.5 Justification Using Two-Scale Convergence II: Proofs.- 3.3 Homogenization of Hyperbolic PDE.- 3.3.1 Textbook Case and Setting.- 3.3.2 Order-0 Homogenization.- 3.3.3 Order-1 Homogenization.- 3.4 Homogenization of Singularly-Perturbed Hyperbolic PDE -- 3.4.1 Equation of Interest and Setting -- 3.4.2 An a Priori Estimate -- 3.4.3 Weak Formulation with Oscillating Test Functions -- 3.4.4 Order-0 Homogenization -- Constraint -- 3.4.5 Order-0 Homogenization -- Equation for V -- 3.4.6 Order-1 Homogenization -- Preparations: Equations for U and u -- 3.4.7 Order-1 Homogenization -- Strong Two-Scale Convergence of u" -- 3.4.8 Order-1 Homogenization -- The Function W1 -- 3.4.9 Order-1 Homogenization -- A Priori Estimate and Convergence -- 3.4.10 Order-1 Homogenization -- Constraint -- 3.4.11 Order-1 Homogenization -- Equation for V1 -- 3.4.12 Concerning Numerics.- II Two-Scale Numerical Methods -- 4 Introduction -- 5 Two-Scale Method for Object Drift with Tide -- 5.1 Motivation and Model -- 5.1.1 Motivation -- 5.1.2 Model of Interest -- 5.2 Two-Scale Asymptotic Expansion -- 5.2.1 Asymptotic Expansion -- 5.2.2 Discussion -- 5.3 Two-Scale Numerical Method -- 5.3.1 Construction of the Two-Scale Numerical Method -- 5.3.2 Validation of the Two-Scale Numerical Method -- 6 Two-Scale Method for Beam -- 6.1 Some Words About Beams and Model of Interest -- 6.1.1 Beams -- 6.1.2 Equations of Interest -- 6.1.3 Two-Scale Convergence -- 6.2 Two-Scale PIC Method -- 6.2.1 Formulation of the Two-Scale Numerical Method -- 6.2.2 Numerical Results.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource (xi, 126 pages), illustrations (some color)
• Subjects: 515/.24; Mathematics; Convergence; Numerical analysis; Convergence; Mathematics -- Number Systems; Numerical analysis; Mathematics; Numerical Analysis; Electronic books
• Languages: English
• ISBNs: 9783319646688; 3319646680; 3319646672; 9783319646671
• Related ISBNs: 9783319646671
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed October 13, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.