Analysis of some moving space-time finite element methods
SIAM Journal on Numerical Analysis
Moving-grid methods for time-dependent partial differential equations
Moving-grid methods for time-dependent partial differential equations
Moving mesh methods based on moving mesh partial differential equations
Journal of Computational Physics
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Moving finite elements
Moving Mesh Methods for Problems with Blow-up
SIAM Journal on Scientific Computing
On the convergence on nonrectangular grids
Journal of Computational and Applied Mathematics
Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
SIAM Journal on Scientific Computing
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
An iterative grid redistribution method for singular problems in multiple dimensions
Journal of Computational Physics
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Symmetric Error Estimates for Moving Mesh Galerkin Methods for Advection-Diffusion Equations
SIAM Journal on Numerical Analysis
Symmetric Error Estimates for Moving Mesh Mixed Methods for Advection-Diffusion Equations
SIAM Journal on Numerical Analysis
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 7.29 |
The stability of three moving-mesh finite-difference schemes is studied in the L^~ norm for one-dimensional linear convection-diffusion equations. These schemes use central finite differences for spatial discretization and the @q method for temporal discretization, and they are based on conservative and non-conservative forms of transformed partial differential equations. The stability conditions obtained consist of the CFL condition and the mesh speed related conditions. The CFL condition is independent of the mesh speed and has the same form as that for fixed meshes. The mesh speed related conditions restrict how fast the mesh can move. The conditions of this type obtained in this paper are weaker than those in the existing literature and can be satisfied when the mesh is sufficiently fine. Illustrative numerical results are presented.