2019
DOI: 10.1002/mma.6049
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The Galerkin spectral element method for the solution of two‐dimensional multiterm time fractional diffusion‐wave equation

Abstract: The aim of this work is to propose an efficient numerical method for the solution of two‐dimensional multiterm time fractional diffusion‐wave equation. The Caputo time fractional derivatives of equation are approximated by a scheme of order scriptOfalse(τ3−αfalse), 1<α<2. To obtain a full‐discrete scheme, we apply the Legendre spectral element method on the spatial direction. Unconditional stability of the semidiscrete scheme and error estimate of full‐discrete method is presented. Numerical experiments are c… Show more

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Cited by 8 publications
(3 citation statements)
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References 30 publications
(67 reference statements)
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“…As is known to all, the spectral element method was yielded by the combination of the finite element method and the spectral method, which means that it incorporates the higherorder accuracy of the spectral method and the geometric flexibility of the finite element scheme. Recently, the spectral element method has been applied for solving FDEs such as the neutral time delay distributed-order fractional damped diffusion-wave equation [44] and the 2D multiterm time-fractional diffusion-wave equation [45]. In 2018, Mao and Shen developed the spectral element method for solving two-sided space FDEs in 1D [46] with geometric mesh.…”
Section: Introductionmentioning
confidence: 99%
“…As is known to all, the spectral element method was yielded by the combination of the finite element method and the spectral method, which means that it incorporates the higherorder accuracy of the spectral method and the geometric flexibility of the finite element scheme. Recently, the spectral element method has been applied for solving FDEs such as the neutral time delay distributed-order fractional damped diffusion-wave equation [44] and the 2D multiterm time-fractional diffusion-wave equation [45]. In 2018, Mao and Shen developed the spectral element method for solving two-sided space FDEs in 1D [46] with geometric mesh.…”
Section: Introductionmentioning
confidence: 99%
“…Since multi-term TFPDEs describe certain diffusion processes more accurately, various numerical methods, including Galerkin FEMs [3,17,50,56], orthogonal spline collocation methods [45], finite difference methods [5,16], compact difference methods [28], spectral methods [47,55], finite volume methods [46] have been developed for such equations. In addition, FEMs [35,36], compact finite difference methods [6,11], finite difference methods [38], Galerkin spectral element methods [6,30], singular boundary methods jointed with dual reciprocity methods [29] are also employed to multi-term TFWEs.…”
Section: Introductionmentioning
confidence: 99%
“…In this useful method, we can implement the finite element method over each element with a priori unknown values at selected spectral nodes 20 . For more information, an interested reader can refer to other studies 20‐24 …”
Section: Introductionmentioning
confidence: 99%