A moving mesh method is developed for the numerical solution of one-dimensional phase-change problems modelled by the phase-field equations. The computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the phase field in the interfacial region. Existence and uniqueness of the discretised equations using a moving mesh are also established....

In this paper, a Godunov scheme on moving meshes, is studied for a kind of timedependent convection-dominated equations with dynamical boundary layers. The rate of convergence in pointwise norm, which is uniform to the small diffusion parameter 2, O(N−1 +τ), is proved, where N is the number of spatial unknowns and τ the mesh size of temporal meshes. This paper is a successful try on the converg...

A new meshing strategy for two-dimensional space-time moving boundary methods is presented. The method breaks the space-time domain into time slabs, and tesselates each sequentially. Within each time slab, the mesh is generated by extruding the lower time plane, moving the boundary, adding and removing vertices near the boundary, and smoothing. Unlike other strategies, topological changes to th...

This paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. The idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. In addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. We also compare th...

In the numerical simulation of the combustion process and microstructural evolution, we need to consider the adaptive meshing problem for a domain with a moving boundary, in which, the submesh in the region behind the moving boundary needs to be coarsened while the submesh in the region ahead of the moving boundary needs to be reened. In this paper, we present a uniied scheme for simultaneously...

Recently a scheme has been proposed for choosing a moving mesh based on minimizing the time rate of change of the solution in the moving coordinates for one-dimensional systems of PDEs. In this paper we show how to apply this idea to systems where the time derivatives cannot be solved for explicitly, writing the moving mesh equations in an implicit form. We give a geometrical interpretation of ...

In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the qualitative behaviour in the blow-up region, and the use of nonuniform meshes is essential. We consider moving mesh methods for which the mesh is determined using so-called m...