TY - JOUR
T1 - A Second-Order Crank-Nicolson Method for Time-Fractional PDEs
AU - Gunzburger , Max
AU - Wang , Jilu
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 225
EP - 239
PY - 2018
DA - 2018/10
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12801.html
KW - Crank-Nicolson scheme, time-fractional equation, convolution quadrature, finite element method, error estimates.
AB - <p style="text-align: justify;">Based on convolution quadrature in time and continuous piecewise linear finite element
approximation in space, a Crank-Nicolson type method is proposed for solving a partial differential
equation involving a fractional time derivative. The method achieves second-order convergence in
time without being corrected at the initial steps. Optimal-order error estimates are derived under
regularity assumptions on the source and initial data but without having to assume regularity of
the solution.</p>