计算数学
計算數學
계산수학
MATHEMATICA NUMERICA SINICA
2010年
1期
15-36
,共22页
双曲型方程%一阶方程组%交替方向有限元方法%收敛性分析%数值试验
雙麯型方程%一階方程組%交替方嚮有限元方法%收斂性分析%數值試驗
쌍곡형방정%일계방정조%교체방향유한원방법%수렴성분석%수치시험
hyperbolic equation%system of first-order equations%Galerkin alternating-direction finite element%convergence analysis%numerical example
对一类一般的三维拟线性双曲型方程通过转化二阶时间导数得到关于一阶时间导数的耦合方程组,然后进行离散得到交替方向有限元格式,应用微分方程先验估计的理论和技巧得到了最优阶H~1-模和L~2-模误差估计,并给出了数值算例,数值结果和理论分析得到很好的吻合.
對一類一般的三維擬線性雙麯型方程通過轉化二階時間導數得到關于一階時間導數的耦閤方程組,然後進行離散得到交替方嚮有限元格式,應用微分方程先驗估計的理論和技巧得到瞭最優階H~1-模和L~2-模誤差估計,併給齣瞭數值算例,數值結果和理論分析得到很好的吻閤.
대일류일반적삼유의선성쌍곡형방정통과전화이계시간도수득도관우일계시간도수적우합방정조,연후진행리산득도교체방향유한원격식,응용미분방정선험고계적이론화기교득도료최우계H~1-모화L~2-모오차고계,병급출료수치산례,수치결과화이론분석득도흔호적문합.
A kind of second-order three-dimensional quasi-linear hyperbolic equation is firstly trans-formed into a system of first-order equations, then the Galerkin alternating-direction proce-dure for the system is derived. The optimal order estimates inH~1 norm and L~2norm of the procedure are obtained respectively by using the theory and techniques of priori estimate of differential equations. The numerical experiment is also given to support the theoretical analysis. Comparison the results of numerical example with the theoretical analysis shows they are uniform.
