本文選題：多尺度有限元法 + Shishkin網(wǎng)格�。� 參考：《揚州大學學報(自然科學版)》2017年01期

【摘要】：針對含變系數(shù)的一維拋物型方程,基于Shishkin網(wǎng)格進行多尺度有限元數(shù)值計算,通過在粗網(wǎng)格上求解微分算子的子問題獲得多尺度基函數(shù)來捕捉局部振蕩信息.利用Shishkin網(wǎng)格分段模擬具有真解的奇異攝動拋物方程邊界層,探討時間尺度的推移對數(shù)值解的穩(wěn)定性與精確性的影響.結(jié)果表明,該方法較經(jīng)典有限元法不但計算精度高、效率高,而且可以節(jié)約計算資源,充分發(fā)揮其數(shù)值優(yōu)勢.
[Abstract]:For the one-dimensional parabolic equation with variable coefficients, the multi-scale finite element numerical calculation based on Shishkin mesh is carried out. The multi-scale basis function is obtained by solving the subproblem of differential operator on rough mesh to capture the local oscillation information.The boundary layer of singularly perturbed parabolic equation with proper solution is simulated by using Shishkin mesh. The effect of time scale on the stability and accuracy of numerical solution is discussed.The results show that this method is more accurate and efficient than the classical finite element method, and it can save calculation resources and give full play to its numerical advantages.
【作者單位】： 揚州大學數(shù)學科學學院;南通大學理學院;
【基金】：國家自然科學基金資助項目(11301462) 江蘇省高校自然科學基金資助項目(13KJB110030) 江蘇省高校青藍工程優(yōu)秀青年骨干教師資助項目
【分類號】：O241.82
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本文編號：1736526