WENO Reconstructions of Unconditionally Optimal High Order

DOI10.1137/18M1229900zbMath1434.65105OpenAlexW2991060196MaRDI QIDQ5203789

Raimund Bürger, Antonio Baeza, Pep Mulet, David Zorío

Publication date: 9 December 2019

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1229900

zbMATH Keywords

critical pointsfinite-difference schemesoptimal orderWENO reconstructions

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items

A novel and robust scale-invariant WENO scheme for hyperbolic conservation laws ⋮ High order weighted essentially non-oscillatory WENO-ZN schemes for hyperbolic conservation laws ⋮ Improving the third-order WENO schemes by using exponential polynomial space with a locally optimized shape parameter ⋮ An Efficient Third-Order WENO Scheme with Unconditionally Optimal Accuracy ⋮ A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations ⋮ Nonlinear weights for shock capturing schemes with unconditionally optimal high order ⋮ Lax-Wendroff approximate Taylor methods with fast and optimized weighted essentially non-oscillatory reconstructions ⋮ Fast and optimal WENO schemes for degenerate parabolic conservation laws ⋮ Three-level order-adaptive weighted essentially non-oscillatory schemes

Cites Work

• Unnamed Item
• Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
• Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues
• Weights design for maximal order WENO schemes
• High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
• Third-order energy stable WENO scheme
• A systematic methodology for constructing high-order energy stable WENO schemes
• Very-high-order WENO schemes
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• Weighted essentially non-oscillatory schemes
• An approximate Lax-Wendroff-type procedure for high order accurate schemes for hyperbolic conservation laws
• Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
• Capturing shock reflections: An improved flux formula
• Efficient implementation of weighted ENO schemes
• An improved weighted essentially non-oscillatory scheme with a new smoothness indicator
• A new mapped weighted essentially non-oscillatory scheme
• An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
• Analysis of WENO Schemes for Full and Global Accuracy
• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• On the Full and Global Accuracy of a Compact Third Order WENO Scheme