scholarly journals An adaptive stabilized finite element scheme for the advection–reaction–diffusion equation

2005 ◽  
Vol 54 (3-4) ◽  
pp. 491-503 ◽  
Author(s):  
Rodolfo Araya ◽  
Edwin Behrens ◽  
Rodolfo Rodríguez
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Stabilized Finite Element

A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation

2020 ◽  
Vol 11 (02) ◽  
pp. 2050016
Author(s):  
Yaping Zhang ◽  
Jiliang Cao ◽  
Weiping Bu ◽  
Aiguo Xiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Time Space ◽  
Distributed Order ◽  
Fractional Reaction ◽  
Element Method

In this work, we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation (2D-DOTSFRDE) with low regularity solution at the initial time. A fast evaluation of the distributed-order time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials. The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed. For the spatial approximation, the finite element method is employed. The convergence of the corresponding fully discrete scheme is investigated. Finally, some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

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