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

Jin-Feng Wang; Min Zhang; Hong Li; Yang Liu

doi:10.11948/2016031

2016 Volume 6 Issue 2

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Jin-Feng Wang, Min Zhang, Hong Li, Yang Liu. FINITE DIFFERENCE/H1-GALERKIN MFE PROCEDURE FOR A FRACTIONAL WATER WAVE MODEL[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 409-428. doi: 10.11948/2016031

Citation:

Jin-Feng Wang, Min Zhang, Hong Li, Yang Liu. FINITE DIFFERENCE/H¹-GALERKIN MFE PROCEDURE FOR A FRACTIONAL WATER WAVE MODEL[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 409-428. doi: 10.11948/2016031

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

1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;
2 School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China

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Abstract

Abstract

In this article, an H¹-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 H¹-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 H¹-norm and L²-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.
- Time fractional water wave model /
- H¹-Galerkin MFE method /
- stability /
- optimal convergence rate /
- a priori error estimates
MSC: 65N30;65M60;35Q10

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References

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