Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems

Tang, Yuelong

doi:10.4236/ajcm.2021.111005

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…Hence, the study of convergence analysis of fractional differential equations has not left untouched. For instance, Tang [8] studied the 246 Convergence Analysis of Space Discretization of Time Fractional Telegraph Equation convergence and superconvergence for the time fractional optimal control problems via a fully discrete finite element scheme. Sontakke and Pandit [9] studied the convergence of nonlinear fractional partial differential equations via the fractional Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis of Space Discretization of Time Fractional Telegraph Equation

Mamadu¹,

Ojarikre²,

Njoseh³

2023

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The role of fractional differential equations in the advancement of science and technology cannot be overemphasized. The time fractional telegraph equation (TFTE) is a hyperbolic partial differential equation (HPDE) with applications in frequency transmission lines such as the telegraph wire, radio frequency, wire radio antenna, telephone lines, and among others. Consequently, numerical procedures (such as finite element method, H 1 -Galerkin mixed finite element method, finite difference method, and among others) have become essential tools for obtaining approximate solutions for these HPDEs. It is also essential for these numerical techniques to converge to a given analytic solution to certain rate. The Ritz projection is often used in the analysis of stability, error estimation, convergence and superconvergence of many mathematical procedures. Hence, this paper offers a rigorous and comprehensive analysis of convergence of the space discretized time-fractional telegraph equation. To this effect, we define a temporal mesh on with a finite element space in Mamadu-Njoseh polynomial space, , of degree An interpolation operator (also of a polynomial space) was introduced along the fractional Ritz projection to prove the convergence theorem. Basically, we have employed both the fractional Ritz projection and interpolation technique as superclose estimate in -norm between them to avoid a difficult Ritz operator construction to achieve the convergence of the method.

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Section: Introductionmentioning

confidence: 99%

Convergence Analysis of Space Discretization of Time Fractional Telegraph Equation

Mamadu¹,

Ojarikre²,

Njoseh³

2023

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show abstract

“…In addition, more researchers found other numerical schemes such as the finite element method [22] and others. Tang has discussed convergence and superconvergence of fully discrete finite element for time fractional optimal control problems [23]. Wang et al have derived the local discontinuous Galerkin method for the Time-Fractional KdV equation [24].…”

Section: Introductionmentioning

confidence: 99%

A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation

Su¹,

Wang²,

Qi³

et al. 2022

JAMP

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In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo's sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction; then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally

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The Coercive Property and a Priori Error Estimation of the Finite Element Method for Linearly Distributed Time Order Fractional Telegraph Equation with Restricted Initial Conditions

Mamadu,

Ojarikre,

Iweobodo

et al. 2024

AJCM

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Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems

Cited by 5 publications

References 25 publications

Convergence Analysis of Space Discretization of Time Fractional Telegraph Equation

Convergence Analysis of Space Discretization of Time Fractional Telegraph Equation

A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation

The Coercive Property and a Priori Error Estimation of the Finite Element Method for Linearly Distributed Time Order Fractional Telegraph Equation with Restricted Initial Conditions

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