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Least‐squares mixed Galerkin formulation for variable‐coefficient fractional differential equations with D‐N boundary condition
Author(s) -
Wang Feng,
Chen Huanzhen,
Wang Hong
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5653
Subject(s) - mathematics , mathematical analysis , constant coefficients , dirichlet boundary condition , boundary value problem , variable (mathematics) , constant (computer programming) , neumann boundary condition , computer science , programming language
We propose a least‐squares mixed variational formulation for variable‐coefficient fractional differential equations (FDEs) subject to general Dirichlet‐Neumann boundary condition by splitting the FDE as a system of variable‐coefficient integer‐order equation and constant‐coefficient FDE. The main contributions of this article are to establish a new regularity theory of the solution expressed in terms of the smoothness of the right‐hand side only and to develop a decoupled and optimally convergent finite element procedure for the unknown and intermediate variables. Numerical analysis and experiments are conducted to verify these findings.