%0 Journal Article %1 zhao2016galerkin %A Zhao, Zhengang %A Zheng, Yunying %A Guo, Peng %D 2016 %J International Journal of Computer Mathematics %K 35r11-fractional-partial-differential-equations 45k05-integro-partial-differential-equations 65m60-pdes-ibvps-finite-elements 65r20-numerical-analysis-integral-equations %N 7 %P 1212--1225 %R 10.1080/00207160.2015.1044986 %T A Galerkin finite element scheme for time-space fractional diffusion equation %U https://www.tandfonline.com/doi/full/10.1080/00207160.2015.1044986 %V 93 %X In this paper, a Galerkin finite element scheme to approximate the time–space fractional diffusion equation is studied. Firstly, the fractional diffusion equation is transformed into a fractional Volterra integro-differential equation. And a second-order fractional trapezoidal formula is used to approach the time fractional integral. Then a Galerkin finite element method is introduced in space direction, where the semi-discretization scheme and fully discrete scheme are given separately. The stability analysis of semi-discretization scheme is discussed in detail. Furthermore, convergence analysis of semi-discretization scheme and fully discrete scheme are given in details. Finally, two numerical examples are displayed to demonstrate the effectiveness of the proposed method.

@article{zhao2016galerkin, abstract = {In this paper, a Galerkin finite element scheme to approximate the time–space fractional diffusion equation is studied. Firstly, the fractional diffusion equation is transformed into a fractional Volterra integro-differential equation. And a second-order fractional trapezoidal formula is used to approach the time fractional integral. Then a Galerkin finite element method is introduced in space direction, where the semi-discretization scheme and fully discrete scheme are given separately. The stability analysis of semi-discretization scheme is discussed in detail. Furthermore, convergence analysis of semi-discretization scheme and fully discrete scheme are given in details. Finally, two numerical examples are displayed to demonstrate the effectiveness of the proposed method.}, added-at = {2024-07-03T01:52:03.000+0200}, author = {Zhao, Zhengang and Zheng, Yunying and Guo, Peng}, biburl = {https://www.bibsonomy.org/bibtex/2865290d28e2d9561e1c303f3bae32da3/gdmcbain}, doi = {10.1080/00207160.2015.1044986}, fjournal = {International Journal of Computer Mathematics}, interhash = {b4e350440cd4427bb07008305db57288}, intrahash = {865290d28e2d9561e1c303f3bae32da3}, issn = {0020-7160}, journal = {International Journal of Computer Mathematics}, keywords = {35r11-fractional-partial-differential-equations 45k05-integro-partial-differential-equations 65m60-pdes-ibvps-finite-elements 65r20-numerical-analysis-integral-equations}, language = {en}, number = 7, pages = {1212--1225}, timestamp = {2024-07-03T01:52:03.000+0200}, title = {A {Galerkin} finite element scheme for time-space fractional diffusion equation}, url = {https://www.tandfonline.com/doi/full/10.1080/00207160.2015.1044986}, volume = 93, year = 2016, zbl = {1390.65122}, zbmath = {6604267} }