| Volume 6, Number 2, 2016, Pages 409-428 DOI：10.11948/2016031 |
| Finite difference/$H^1$-Galerkin MFE procedure for a fractional water wave model |
| Jin-Feng Wang,Min Zhang,Hong Li,Yang Liu |
| Keywords:Time fractional water wave model, $H^1$-Galerkin MFE method, stability, optimal convergence rate, a priori error estimates |
| Abstract: |
| In this article, an $H^1$-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 $H^1$-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 $H^1$-norm and $L^2$-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 |
PDF Download reader
|
|
|
|