In this paper a time-dependent moving-grid method is described to numerically solve time-dependent partial differential equations (PDEs) in one space dimensions involving fine scale structures such as steep moving fronts, emerging steep layers, pulses and shocks. Smoothing in the spatial direction is employed to control grid clustering and expansion. Additional smoothing in the temporal directi...

in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

in this paper, based on the slab method of analysis, a novel and general approach isdeveloped for studying the radial forging process with curved profile dies. the presented approachis not only more general with respect to previous studies, but it is also easier to understand and useand can be efficiently used for optimization of the die profile depending on the forging geometryand conditions. ...