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Journal of Scientific Computing

Erschienen in:

16.11.2018

Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach

verfasst von: Zhaopeng Hao, Moongyu Park, Guang Lin, Zhiqiang Cai

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2019

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Abstract

This paper develops a Galerkin approach for two-sided fractional differential equations with variable coefficients. By the product rule, we transform the problem into an equivalent formulation which additionally introduces the fractional low-order term. We prove the existence and uniqueness of the solutions of the Dirichlet problems of the equations with certain diffusion coefficients. We adopt the Galerkin formulation, and prove its error estimates. Finally, several numerical examples are provided to illustrate the fidelity and accuracy of the proposed theoretical results.

Vorheriger Artikel Accelerated Alternating Direction Method of Multipliers: An Optimal O(1 / K) Nonergodic Analysis

Nächster Artikel Physics-Based Balancing Domain Decomposition by Constraints for Multi-Material Problems

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Titel: Finite Element Method for Two-Sided Fractional Differential Equations with Variable Coefficients: Galerkin Approach
verfasst von: Zhaopeng Hao
Moongyu Park
Guang Lin
Zhiqiang Cai
Publikationsdatum: 16.11.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0869-5

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