A moving mesh method for the solution of the one-dimensional phase-field equations
Journal of Computational Physics
A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows
Journal of Computational Physics
Tensor-product adaptive grids based on coordinate transformations
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Efficient computation of dendritic growth with r-adaptive finite element methods
Journal of Computational Physics
Convergence analysis of moving Godunov methods for dynamical boundary layers
Computers & Mathematics with Applications
Optimal mass transport for higher dimensional adaptive grid generation
Journal of Computational Physics
Moving mesh method for problems with blow-up on unbounded domains
Numerical Algorithms
Adaptive numerical simulation of traffic flow density
Computers & Mathematics with Applications
| Hi-index | 0.02 |
Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh method of Dorfi and Drury [J. Comput. Phys., 69 (1987), pp. 175--195]. It is shown that under weak conditions the basic property of no node-crossing is preserved by the spatial smoothing, and a local quasi-uniformity property of the coordinate transformations determined by these MMPDEs is proven. It is also shown that, discretizing the MMPDEs using centered finite differences, these basic properties are preserved.