Finite Element Method for a Nonlinear Differential Equation Describing Crystal Surface Growth

Abstract

In this paper, for a nonlinear differential equation describing crystal surface growth, the finite element method is presented. A nice order error estimates is derived by means of a finite element projection approximation.

A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient

“…where Du = ∂u ∂x . We give the existence of the solution of problem (8) in the following theorem (see [12]). Theorem 2.1 Suppose that u 0 ∈ H 2 0 (I).…”

“…This limit turned out to be singular, and nonlinearities of arbitrary order need to be taken into account. For 1D case of equation 3, Zhao et al proved that the Hermite finite element method has the convergence rate of O( t + h 3 ) (see [12]).…”

On the Classical Solutions for the Kuramoto-Sivashinsky Equation with Ehrilch-Schwoebel Effects

“…In particular, the authors studied the initial-boundary value problem. Numerical techniques like finite difference, finite element and kinetic Monte Carlo method were used to provide approximate solutions to the equation describing crystal surface growth [25][26][27][28]. The pyramidal structure characterized by the absence of preferred slope in onedimension was examined in [29], applying a similarity approach.…”

Instabilities in certain one-dimensional singular interfacial equation

“…Global solutions were constructed to the parabolic evolution equation by Fujimura and Yagi [23]. Numerical techniques like finite difference, finite element and kinetic Monte Carlo method were used to provide approximate solutions to the equation describing crystal surface growth [24][25][26][27]. The pyramidal structure characterized by the absence of preferred slope in one-dimension was examined by Guedda and Trojette [28] applying a similarity approach.…”