A level set moving mesh method in static form for one dimensional PDEs

In this paper, we propose an adaptive mesh approach for time dependent parial differential equations, based on a so-called moving mesh pde(mmpde) and level set method. it means that the velocity of mesh nodes is calculated by mmpdeand is employed as veocity in the level set equation. then, at each time level, the mesh points are considered as the level contours of the level set function. finally the method is merged with local time step technique.