High-order weighted compact nonlinear scheme for solving degenerate parabolic equations

DOI10.1007/s40314-023-02551-zMaRDI QIDQ6192337

Xiao Qian Huang, Ying-Gang Hu, Wei Zhang, Yan-Qun Jiang

Publication date: 12 February 2024

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear degenerate parabolic equationshigh-order accurateweighted compact nonlinear schemenon-oscillatory propertydiscontinuity-capturing ability

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Cites Work

• Unnamed Item
• A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations
• High order operator splitting methods based on an integral deferred correction framework
• An adaptive SUPG method for evolutionary convection-diffusion equations
• A new class of central compact schemes with spectral-like resolution. II: Hybrid weighted nonlinear schemes
• Development of nonlinear weighted compact schemes with increasingly higher order accuracy
• An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source
• Adaptive multiresolution schemes with local time stepping for two-dimensional degenerate reaction-diffusion systems
• Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
• A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying geometric conservation law
• Robust explicit formulation of weighted compact nonlinear scheme
• High order finite difference multi-resolution WENO method for nonlinear degenerate parabolic equations
• A new type of high-order finite difference compact reconstruction multi-resolution WENO scheme for nonlinear degenerate parabolic equations
• A RBF-WENO finite difference scheme for non-linear degenerate parabolic equations
• A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows
• High order implicit finite difference schemes with a semi-implicit WENO reconstruction for nonlinear degenerate parabolic equations
• Finite volume WENO schemes for nonlinear parabolic problems with degenerate diffusion on non-uniform meshes
• Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing
• High-order weighted compact nonlinear scheme for one- and two-dimensional Hamilton-Jacobi equations
• Numerical dissipation control in an adaptive WCNS with a new smoothness indicator
• ANALYSIS OF THE SPACE SEMI-DISCRETIZED SUPG METHOD FOR TRANSIENT CONVECTION–DIFFUSION EQUATIONS
• High Order Finite Difference WENO Schemes for Nonlinear Degenerate Parabolic Equations
• Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
• A numerical method for solving the problem $u_t - \Delta f (u) = 0$
• A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations
• Developing high-order weighted compact nonlinear schemes
• A high‐order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations
• A new high‐order weighted essentially non‐oscillatory scheme for non‐linear degenerate parabolic equations