Year: 2019
Author: Max Gunzburger, Jilu Wang
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 225–239
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12801
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 225–239
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Crank-Nicolson scheme time-fractional equation convolution quadrature finite element method error estimates.