Property-preserving Numerical Schemes For Conservation Laws
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A01=Dmitri Kuzmin
A01=Hennes Hajduk
Age Group_Uncategorized
Age Group_Uncategorized
Algebraic Flux Correction
Approximate Riemann Solvers
Artificial Diffusion
Author_Dmitri Kuzmin
Author_Hennes Hajduk
automatic-update
Barth-Jespersen Limiter
Bernstein Polynomials
Category1=Non-Fiction
Category=PBKS
Category=PBMB
Category=PBW
Category=PHDF
Continuous Galerkin Method
Convex Limiting
COP=Singapore
Delivery_Delivery within 10-20 working days
Discontinuous Galerkin Method
Discontinuous Galerkin Spectral Element Method
Discrete Upwinding
Entropy Inequalities
Entropy Stability
eq_isMigrated=0
eq_isMigrated=2
eq_nobargain
Euler Equations
Finite Element Methods
Finite Volume Methods
Flux Limiting
Flux-Corrected Remapping
Flux-Corrected Transport
Godunov-Type Methods
High-Order Methods
Hyperbolic Conservation Laws
Invariant Domains
Language_English
Legendre-Gauss-Lobatto Quadrature
Local Extremum Diminishing Schemes
Maximum Principles
MUSCL Schemes
PA=Available
Polynomial Reconstruction
Positivity Preservation
Price_€100 and above
PS=Active
Shallow Water Equations
Shock Capturing
Slope Limiting
Smoothness Indicator
softlaunch
Spatially Partitioned Runge-Kutta Methods
Stabilization
Strong Stability Preserving Runge-Kutta Methods
Taylor Basis
Total Variation Diminishing Schemes
Transport Equations
Unstructured Meshes
Vertex-Based Slope Limiter
Weighted Essentially Non-Oscillatory Schemes
Zalesak's Limiter
Product details
- ISBN 9789811278181
- Publication Date: 13 Sep 2023
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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High-order numerical methods for hyperbolic conservation laws do not guarantee the validity of constraints that physically meaningful approximations are supposed to satisfy. The finite volume and finite element schemes summarized in this book use limiting techniques to enforce discrete maximum principles and entropy inequalities. Spurious oscillations are prevented using artificial viscosity operators and/or essentially nonoscillatory reconstructions.An introduction to classical nonlinear stabilization approaches is given in the simple context of one-dimensional finite volume discretizations. Subsequent chapters of Part I are focused on recent extensions to continuous and discontinuous Galerkin methods. Many of the algorithms presented in these chapters were developed by the authors and their collaborators. Part II gives a deeper insight into the mathematical theory of property-preserving numerical schemes. It begins with a review of the convergence theory for finite volume methods and ends with analysis of algebraic flux correction schemes for finite elements. In addition to providing ready-to-use algorithms, this text explains the design principles behind such algorithms and shows how to put theory into practice. Although the book is based on lecture notes written for an advanced graduate-level course, it is also aimed at senior researchers who develop and analyze numerical methods for hyperbolic problems.
