FINITE DIFFERENCE/H1-GALERKIN MFE PROCEDURE FOR A FRACTIONAL WATER WAVE MODEL | Zendy

Jinfeng Wang | Zendy; Min Zhang | Zendy; Hong Li | Zendy; Yang Liu | Zendy

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FINITE DIFFERENCE/<i>H</i><sup>1</sup>-GALERKIN MFE PROCEDURE FOR A FRACTIONAL WATER WAVE MODEL

Author(s) -

Jinfeng Wang,

Min Zhang,

Hong Li,

Yang Liu

Publication year - 2016

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2016031

Subject(s) - mathematics , mathematical analysis , norm (philosophy) , finite element method , galerkin method , discontinuous galerkin method , fractional calculus , physics , political science , law , thermodynamics

In this article, an H-Galerkin mixed finite element (MFE) method for solving the time fractional water wave model is presented. First-order backward Euler difference method and L1 formula are applied to approximate integer derivative and Caputo fractional derivative with order 1/2, respectively, and H-Galerkin mixed finite element method is used to approximate the spatial direction. The analysis of stability for fully discrete mixed finite element scheme is made and the optimal space-time orders of convergence for two unknown variables in both H-norm and L-norm are derived. Further, some computing results for a priori analysis and numerical figures based on four changed parameters in the studied problem are given to illustrate the effectiveness of the current method.

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