TY - JOUR
T1 - Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation
AU - Zhang , Na
AU - Deng , Weihua
AU - Wu , Yujiang
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 496
EP - 518
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m1210
UR - https://global-sci.org/intro/article_detail/aamm/133.html
KW - Modified subdiffusion equation, finite difference method, finite element method,
stability, convergence rate.
AB - <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>