Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
Alternating Direction Implicit Galerkin Methods for an Evolution Equation with a Positive-Type Memory Term
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DOI：
10.1007/s10915-015-0004-9
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发表时间：
2015-12
影响因子：
2.5
通讯作者：
M. Khebchareon;A. K. Pani;G. Fairweather
中科院分区：
文献类型：
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作者：
M. Khebchareon;A. K. Pani;G. Fairweather
我们制定和分析新的方法解决偏积分微分方程的正型记忆项。这些方法结合了联合收割机的有限元Galerkin（FEG）方法的空间离散与交替方向隐式（ADI）方法的基础上的Crank-Nicolson（CN）方法和二阶向后微分公式的时间步进。ADI FEG方法在时间和空间上都具有最佳精度。此外，该分析还扩展到包括针对非光滑核问题的具有时间分级网格的ADI CN FEG方法。数值结果证实了预测的收敛速度，也表现出最佳的空间精度的thumerm。
We formulate and analyze new methods for the solution of a partial integrodifferential equation with a positive-type memory term. These methods combine the finite element Galerkin (FEG) method for the spatial discretization with alternating direction implicit (ADI) methods based on the Crank–Nicolson (CN) method and the second order backward differentiation formula for the time stepping. The ADI FEG methods are proved to be of optimal accuracy in time and in thenorm in space. Furthermore, the analysis is extended to include an ADI CN FEG method with a graded mesh in time for problems with a nonsmooth kernel. Numerical results confirm the predicted convergence rates and also exhibit optimal spatial accuracy in thenorm.