A New Finite Element Analysis for Inhomogeneous Boundary-Value Problems of Space Fractional Differential Equations

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• 作者：Jingtang Ma
• 关键词：Fractional differential equations ; Galerkin methods ; Finite element methods ; Convergence analysis
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：70
• 期：1
• 页码：342-354
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

In this paper the framework and convergence analysis of finite element methods (FEMs) for space fractional differential equations (FDEs) with inhomogeneous boundary conditions are studied. Since the traditional framework of Gakerkin methods for space FDEs with homogeneous boundary conditions is not true any more for the case of inhomogeneous boundary conditions, this paper develops a technique by introducing a new fractional derivative space in which the Galerkin method works and proves the convergence rates of the FEMs.