Fast and optimal WENO schemes for degenerate parabolic conservation laws

DOI10.1007/S10915-021-01689-4zbMath1481.65126OpenAlexW3217090057MaRDI QIDQ2053383

Yanyan Li

Publication date: 29 November 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-021-01689-4

zbMATH Keywords

degenerate diffusionweighted essentially non-oscillatory (WENO) methodsparabolic conservation lawsoptimized weights

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Diffusion (76R50) Degenerate parabolic equations (35K65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (2)

Convergence of entropy stable schemes for degenerate parabolic equations with a discontinuous convection term ⋮ High-order entropy stable schemes based on a local adaptive WENO viscosity for degenerate convection-diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations
• Weights design for maximal order WENO schemes
• Numerical simulation for porous medium equation by local discontinuous Galerkin finite element method
• A systematic methodology for constructing high-order energy stable WENO schemes
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Weighted essentially non-oscillatory schemes on triangular meshes
• Weighted essentially non-oscillatory schemes
• Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
• Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
• On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients
• Efficient implementation of weighted ENO schemes
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Lax-Wendroff approximate Taylor methods with fast and optimized weighted essentially non-oscillatory reconstructions
• Finite volume WENO schemes for nonlinear parabolic problems with degenerate diffusion on non-uniform meshes
• On the efficient computation of smoothness indicators for a class of WENO reconstructions
• On an upwind difference scheme for strongly degenerate parabolic equations modelling the settling of suspensions in centrifuges and non-cylindrical vessels
• A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solutions
• Strong Stability-Preserving High-Order Time Discretization Methods
• Entropy Stable Schemes for Degenerate Convection-Diffusion Equations
• Analysis of WENO Schemes for Full and Global Accuracy
• High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
• Monotone Difference Approximations Of BV Solutions To Degenerate Convection-Diffusion Equations
• Difference schemes stabilized by discrete mollification for degenerate parabolic equations in two space dimensions
• An unconditionally stable splitting scheme for a class of nonlinear parabolic equations
• An Efficient Third-Order WENO Scheme with Unconditionally Optimal Accuracy
• WENO Reconstructions of Unconditionally Optimal High Order
• Operator splitting methods for degenerate convection-diffusion equations. II: Numerical examples with emphasis on reservoir simulation and sedimentation
• A technique of treating negative weights in WENO schemes

This page was built for publication: Fast and optimal WENO schemes for degenerate parabolic conservation laws