Work

A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection

Year: 2019

Type: preprint

Abstract: In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term $Aτ^2\frac{\partialΔ^2 u}{\partial t}$ is added to the physical model to achieve energy stability, with ETD-based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed $\ell^{\infty}(0,T; \ell^2)$ error analysis are provided based on the energy method, with a careful estimate of the aliasing error. In addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1907.02234

Authors: Chen, Wenbin, Li, Weijia, Luo, Zhiwen, Wang, Cheng, Wang, Xiaoming

Institutions: Fudan University, University of Massachusetts Dartmouth, Florida State University, Southern University of Science and Technology

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China, Fudan University

Awards: G2945020083, G3734671938, Some Mathematical Problems Associated with Hyporheic Flow, G4969315547, G53304062, Highly efficient and accurate numerical schemes for nonlinear gradient flows with energy stability, G7071190101

OpenAlex ID: W2954504234

Cites: 40

Cited by: 4

Related to: 10