@Article{AAMM-4-4,
author = {Zhang, Na and Weihua, Deng and Yujiang, Wu},
title = {Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {4},
pages = {496--518},
abstract = {<p style="text-align: justify;">We present the finite difference/element method for a
two-dimensional modified fractional diffusion equation. The analysis
is carried out first for the time semi-discrete scheme, and then for
the full discrete scheme. The time discretization is based on the
$L1$-approximation for the fractional derivative terms and the
second-order backward differentiation formula for the classical
first order derivative term. We use finite element method for the
spatial approximation in full discrete scheme. We show that both the
semi-discrete and full discrete schemes are unconditionally stable
and convergent. Moreover, the optimal convergence rate is obtained.
Finally, some numerical examples are tested in the case of one and
two space dimensions and the numerical results confirm our
theoretical analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m1210},
url = {https://global-sci.com/article/73556/finite-differenceelement-method-for-a-two-dimensional-modified-fractional-diffusion-equation}
}