10 research outputs found
Recommended from our members
Finite element approximation of a sixth order nonlinear degenerate parabolic equation
We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)?
2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented
Qualitative properties for a sixth–order thin film equation
In this article, the author studies the qualitative properties of weak solutions for a sixth‐order thin film equation, which arises in the industrial application of the isolation oxidation of silicon. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the expansion of the support of solutions are also discussed.
First published online: 10 Feb 201
The conforming virtual element method for polyharmonic and elastodynamics problems: a review
In this paper, we review recent results on the conforming virtual element
approximation of polyharmonic and elastodynamics problems. The structure and
the content of this review is motivated by three paradigmatic examples of
applications: classical and anisotropic Cahn-Hilliard equation and phase field
models for brittle fracture, that are briefly discussed in the first part of
the paper. We present and discuss the mathematical details of the conforming
virtual element approximation of linear polyharmonic problems, the classical
Cahn-Hilliard equation and linear elastodynamics problems.Comment: 30 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1912.0712
Finite element approximation of a phase field model for void electromigration
We consider a fully practical finite element approximation of the nonlinear degenerate parabolic syste