A linearized finite difference scheme for the Richards equation under variable-flux boundary conditions

DOI10.1007/s10915-020-01196-yzbMath1433.76113OpenAlexW3013129702MaRDI QIDQ2173570

Yasuhide Fukumoto, Xiaopeng Zhao, Liu Fengnan

Publication date: 16 April 2020

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

Full work available at URL: https://doi.org/10.1007/s10915-020-01196-y

zbMATH Keywords

stabilityfinite difference schemeerror estimateRichards equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Flows in porous media; filtration; seepage (76S05) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (3)

A multi level linearized Crank–Nicolson scheme for Richards equation under variable flux boundary conditions ⋮ Unnamed Item ⋮ Second order monotone finite-difference schemes on non-uniform grids for multi-dimensional convection-diffusion problem with a boundary condition of the third kind

Cites Work

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• Spectral properties and conservation laws in mimetic finite difference methods for PDEs
• Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
• Infiltration from supply at constant water content: An integrable model
• Finite difference discretization of the Kuramoto-Sivashinsky equation
• A method for the numerical solution of a class of nonlinear diffusion equations
• A study on iterative methods for solving Richards' equation
• Analysis of a fourth-order finite difference method for the incompressible Boussinesq equations
• The finite volume method for Richards equation
• The numerical solution of Richards' equation by means of method of lines and ensemble Kalman filter
• An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation
• A compact fourth-order finite difference scheme for the three-dimensional Cahn-Hilliard equation
• Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
• Order of Convergence Estimates for an Euler Implicit, Mixed Finite Element Discretization of Richards' Equation
• A Consistent Fourth-Order Compact Finite Difference Scheme for Solving Vorticity-Stream Function Form of Incompressible Navier-Stokes Equations
• Fourth Order Finite Difference Methods for the Wave Equation with Mesh Refinement Interfaces

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