An extension of the discrete variational method to nonuniform grids

DOI10.1016/j.jcp.2010.02.018zbMath1190.65128OpenAlexW2073550403MaRDI QIDQ974311

Masaaki Sugihara, Takayasu Matsuo, Takaharu Yaguchi

Publication date: 27 May 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.02.018

zbMATH Keywords

numerical examplesdissipationfinite difference schemesKorteweg-de Vries equationconservationmapping methoddiscrete variational methodnonuniform meshCahn-Hillard equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

Conservative finite volume element schemes for the complex modified Korteweg-de Vries equation, A note on the adaptive conservative/dissipative discretization for evolutionary partial differential equations, A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations, Energy-preserving schemes for conservative PDEs based on periodic quasi-interpolation methods, The discrete variational derivative method based on discrete differential forms, Invariants-preserving integration of the modified Camassa-Holm equation, Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method, A general framework for finding energy dissipative/conservative \(H^1\)-Galerkin schemes and their underlying \(H^1\)-weak forms for nonlinear evolution equations, New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation, Post processing of solution and flux for the nodal mimetic finite difference method, Discrete variational derivative method—A structure-preserving numerical method for partial differential equations, Adaptive energy preserving methods for partial differential equations, A local discontinuous Galerkin method based on variational structure, New conservative finite volume element schemes for the modified Korteweg–de Vries equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New conservative schemes with discrete variational derivatives for nonlinear wave equations
• Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations
• A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation
• Spatially accurate dissipative or conservative finite difference schemes derived by the discrete variational method
• Mimetic finite difference methods for diffusion equations
• A conservative difference scheme for the viscous Cahn--Hilliard equation with a nonconstant gradient energy coefficient
• Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Conservative Finite-Difference Methods on General Grids
• A Higher-Order Formulation of the Mimetic Finite Difference Method
• Spectral residual method without gradient information for solving large-scale nonlinear systems of equations
• Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• A stable and conservative finite difference scheme for the Cahn-Hilliard equation
• Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations