具有真解的一维抛物方程在Shishkin网格上的多尺度计算

发布时间：2018-04-11 15:15

  本文选题：多尺度有限元法 + Shishkin网格　； 参考：《扬州大学学报(自然科学版)》2017年01期

【摘要】：针对含变系数的一维抛物型方程,基于Shishkin网格进行多尺度有限元数值计算,通过在粗网格上求解微分算子的子问题获得多尺度基函数来捕捉局部振荡信息.利用Shishkin网格分段模拟具有真解的奇异摄动抛物方程边界层,探讨时间尺度的推移对数值解的稳定性与精确性的影响.结果表明,该方法较经典有限元法不但计算精度高、效率高,而且可以节约计算资源,充分发挥其数值优势.
[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.
【作者单位】： 扬州大学数学科学学院;南通大学理学院;
【基金】：国家自然科学基金资助项目(11301462) 江苏省高校自然科学基金资助项目(13KJB110030) 江苏省高校青蓝工程优秀青年骨干教师资助项目
【分类号】：O241.82
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本文编号：1736526