Numerical Methods for Conservation Laws: From Analysis to Algorithms
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Summary
This course develops, analyse and apply computational methods suitable for solving systems of conservation laws, including Godunov's methods, monotone fluxes, accuracy, and stability of such methods, and develops discontinuous Galerkin methods as a very general and robust high-order accurate extension of finite volume methods.
- Type
- book
- Published
- 2017-12-21
- Cited by
- 1,991
- References
- 304
- Access
- Open access
- OpenAlex
- https://openalex.org/W2782116534
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:122111414
Keywords
Conservation law, Law, Numerical analysis, Political science, Computer science
References
- Padé–Jacobi Filtering for Spectral Approximations of Discontinuous Solutions
- Triangular mesh methods for the neutron transport equation
- Understanding the Shu–Osher Conservative Finite Difference Form
- Spectral methods for time dependent problems
- Accurate partial difference methods
- High order well-balanced schemes
- A SLOPE LIMITING PROCEDURE IN DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR GASDYNAMICS APPLICATIONS
- Numerical Solution of Hyperbolic Partial Differential Equations
- Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer
- Strong stability preserving runge-kutta and multistep time discretizations
- The Mathematical Theory of Finite Element Methods
- Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
- Accuracy of High Order and Spectral Methods for Hyperbolic Conservation Laws with Discontinuous Solutions
- Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- Time-Dependent Problems and Difference Methods
- Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids III: One Dimensional Systems and Partition Optimization
- An introduction to computational fluid dynamics - the finite volume method
- One-sided difference approximations for nonlinear conservation laws
- On the Conservation and Convergence to Weak Solutions of Global Schemes
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