Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016
Published on 26. October 2017
VIII, 211 pages
978-3-319-67202-1 (ISBN)
Description
This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena.
The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between
these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics.
This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app
roximation of solutions of singularly perturbed differential equations; that is, problems whose solutions exhibit boundary and/or interior layers.More details
Series
Edition
1st ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
VIII, 211 p. 61 illus., 52 illus. in color.
File size
9,69 MB
ISBN-13
978-3-319-67202-1 (9783319672021)
DOI
10.1007/978-3-319-67202-1
Schweitzer Classification
Other editions
Additional editions
Zhongyi Huang | Martin Stynes | Zhimin Zhang
Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016
Book
10/2017
Springer
€106.99
Shipment within 10-15 days
Content
- Intro
- Preface
- Contents
- Error Estimates in Balanced Norms of Finite Element Methods on Layer-Adapted Meshes for Second Order Reaction-Diffusion Problems
- 1 Introduction
- 2 The Basic Error Estimate in a Balanced Norm and Some Extensions
- 2.1 Linear Problems
- 2.2 Semilinear Problems
- 2.3 An Anisotropic Diffusion Problem
- 3 The 3D Case and Different Classes of Layer-Adapted Meshes
- 3.1 The 3D Case
- 3.2 Different Classes of Layer-Adapted Meshes
- 4 Supercloseness and a Combination Technique
- 5 A Direct Mixed Method
- 6 Remarks and Further Open Problems
- References
- Numerical Studies of Higher Order Variational Time Stepping Schemes for Evolutionary Navier-Stokes Equations
- 1 Introduction
- 2 Model Problem and Its Finite Element Discretization
- 3 Variational Time-Stepping Schemes
- 3.1 The Continuous Galerkin-Petrov Method
- 3.2 The Discontinuous Galerkin Method
- 3.3 Post-Processing
- 4 Numerical Results
- References
- Uniform Convergent Monotone Iterates for Nonlinear Parabolic Reaction-Diffusion Systems
- 1 Introduction
- 2 The Nonlinear Difference Scheme
- 3 The Monotone Iterative Method
- 3.1 Convergence on [0,T]
- 3.2 Construction of Initial Upper and Lower Solutions
- 4 Uniform Convergence of the Monotone Iterates
- 5 Gas-Liquid Interaction Model
- References
- Order Reduction and Uniform Convergence of an Alternating Direction Method for Solving 2D Time Dependent Convection-Diffusion Problems
- 1 Introduction
- 2 Spatial Discretization
- 3 Time Discretization: Uniform Convergence
- 4 Numerical Experiments
- References
- Laminar Boundary Layer Flow with DBD Plasma Actuation: A Similarity Equation
- 1 Introduction
- 2 Flow with Idealized DBD Plasma Actuation
- 2.1 Boundary Layer Equations with Force Terms
- 3 Similarity Form of the Boundary Layer Equations
- 3.1 Relation Between Flow Components
- 3.2 Transformation of Flow Variables
- 3.3 Similarity Conditions
- 3.3.1 Blasius Flow
- 3.3.2 Falkner-Skan Flow
- 3.3.3 Actuated Flow with Pressure Gradient
- 4 Numerical Solutions of the Similarity Equation
- 5 Applications and Future Research
- References
- On Robust Error Estimation for Singularly Perturbed Fourth-Order Problems
- 1 Introduction
- 2 Numerical Analysis
- 2.1 Solution Decomposition and Meshes
- 2.2 Error Estimation in L8
- 2.3 Postprocessing
- 3 Numerical Experiments
- References
- Singularly Perturbed Initial-Boundary Value Problemswith a Pulse in the Initial Condition
- 1 Introduction
- 2 Reaction-Diffusion Problem
- 3 Bounds on the Derivatives of the Continuous Solution
- 4 Numerical Method and Error Analysis
- 5 Numerical Experiments
- References
- Numerical Results for Singularly Perturbed Convection-Diffusion Problems on an Annulus
- 1 Introduction
- 2 Continuous Problem
- 3 Discrete Problem and Numerical Results
- 4 The Hemker Problem
- 5 Conclusions
- References
- Numerical Calculation of Aerodynamic Noise Generated from an Aircraft in Low Mach Number Flight
- 1 Introduction
- 2 Proposed Methodology to Simulate Aerodynamic Noise
- 3 Orthogonal Subgrid Scale Method with Dynamical Subscales
- 4 Model and Simulation Setup
- 5 Comparison of Results for Two Turbulent Models and Their Effect on Aeroacoustic Sources and Acoustic Propagation
- 6 Discussion and Conclusion
- References
- On the Discrete Maximum Principle for Algebraic Flux Correction Schemes with Limiters of Upwind Type
- 1 Introduction
- 2 An Algebraic Flux Correction Scheme
- 3 A General Result on the Discrete Maximum Principle
- 4 Validity of the DMP for Particular Limiters
- 5 Upwind Character of the Limiters
- References
- Energy-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes: Neumann Boundary Conditions
- 1 Introduction
- 2 Basic Triangulation Assumptions: Scaled Trace Bounds
- 3 Representation of the Error in Terms of the Residual
- 4 Error Analysis for a Partially Structured Anisotropic Mesh
- 4.1 Choice of z: Main Results
- 4.2 Jump Residual: Proof of (20) and (21)
- 5 Numerical Results
- References
- A DG Least-Squares Finite Element Method for Nagumo's Nerve Equation with Fast Reaction: A Numerical Study
- 1 Introduction
- 2 A DG LSFE Scheme
- 3 Numerical Simulations and Discussions
- 4 Conclusions
- References
- Local Projection Stabilization for Convection-Diffusion-Reaction Equations on Surfaces
- 1 Introduction
- 2 Problem Formulation
- 3 Discretization
- 3.1 Surface Approximation
- 3.2 Extension of Data
- 3.3 Discrete Problem
- 4 Local Projection Stabilization
- 5 Numerical Results
- 5.1 Testcase 1: Layer in the First Derivative
- 5.2 Testcase 2: Exponential Layer in the Solution
- 5.3 Testcase 3: Layer on a Sphere
- References
- A Comparison Study of Parabolic Monge-Ampère Equations Adaptive Grid Methods
- 1 Introduction
- 2 The L2 Monge-Kantorovich Problem
- 3 The Parabolic Monge-Ampére Adaptive Grid Methods
- 3.1 PMA-Log Adaptive Grid Method
- 3.2 PMA-Sqrt Adaptive Grid Method
- 4 Numerical Experiments
- 4.1 Example 1
- 4.2 Example 2
- 4.3 Example 3
- 5 Conclusion
- References
- Approximate Solutions to Poisson Equation Using Least Squares Support Vector Machines
- 1 Introduction
- 2 Brief Introduction to the Modified LS-SVM Regression
- 3 Formulation of the Method for Poisson Equation
- 4 Numerical Experiments
- 5 Conclusions
- References
