【摘要】：本文針對(duì)一維Cahn-Hilliard方程,提出了一種直接間斷有限元方法,證明了直接間斷有限元格式的保質(zhì)量守恒性質(zhì)和保能量衰減性質(zhì)。對(duì)三種有限差分法(Crank-Nicolson Adams-Bashforth方法、基于DVDM的FDM、基于Picard迭代的FDM)和直接間斷有限元方法進(jìn)行了數(shù)值比較,我們通過(guò)數(shù)值算例驗(yàn)證了每種數(shù)值格式能夠保證質(zhì)量守恒以及能量衰減,也發(fā)現(xiàn),當(dāng)時(shí)間離散選用向前歐拉時(shí),直接間斷有限元方法的時(shí)間步長(zhǎng)需要取得較小。
[Abstract]:In this paper, a direct discontinuous finite element method is proposed for one dimensional Cahn-Hilliard equation. The conservation of mass and energy conservation of direct discontinuous finite element scheme are proved. Three finite difference methods (Crank-Nicolson Adams-Bashforth method, FDM, based on Picard iteration FDM based on DVDM) and direct discontinuous finite element method (DFEM) are compared numerically. Numerical examples show that each numerical scheme can guarantee the conservation of mass and energy attenuation. It is also found that the time step of direct discontinuous finite element method needs to be smaller when the time discretization is forward Euler.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O241.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 Ting-chun WANG;Li-mei ZHAO;Bo-ling GUO;;A Class of Stable and Conservative Finite Difference Schemes for the Cahn-Hilliard Equation[J];Acta Mathematicae Applicatae Sinica;2015年04期

2 葉興德,程曉良;Cahn—Hilliard方程的Legendre譜逼近[J];計(jì)算數(shù)學(xué);2003年02期

，

本文編號(hào)：2321088