scholarly journals Second-order time discretization with finite-element method for partial integro-differential equations with a weakly singular kernel

1999 ◽  
Vol 40 (4) ◽  
pp. 513-524
Author(s):  
Chang Ho Kim ◽  
U Jin Choi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Time Discretization ◽  
Second Order ◽  
Singular Kernel ◽  
Element Approximation ◽  
Weakly Singular Kernel ◽  
Weakly Singular ◽  
Element Method

AbstractWe propose the second-order time discretization scheme with the finite-element approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the finite element method and the time discretization is based on the Crank-Nicolson scheme with a graded mesh. We show the stability of the scheme and obtain the second-order convergence result for the fully discretized scheme.

scholarly journals Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jingjun Zhao ◽  
Jingyu Xiao ◽  
Yang Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Discretization ◽  
Stability And Convergence ◽  
Fractional Partial Differential Equations ◽  
Weak Formulation ◽  
Partial Differential ◽  
Element Method

A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions.

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