Least‐squares mixed Galerkin formulation for variable‐coefficient fractional differential equations with D‐N boundary condition

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 co...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 42; no. 12; pp. 4331 - 4342
Main Authors Wang, Feng, Chen, Huanzhen, Wang, Hong
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 01.08.2019
Subjects
Boundary conditions
Coefficients
Differential equations
Dirichlet problem
Finite element method
fractional diffusion equation
Galerkin method
least‐squares
mixed variational formulation
Numerical analysis
optimal convergence
regularity
Smoothness
variable‐coefficient
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ISSN0170-4214
1099-1476
DOI10.1002/mma.5653

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Summary: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.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5653