The ultra-weak discontinuous Galerkin method for time-fractional Burgers equation

A ultra-weak discontinuous Galerkin finite element method for a series of time-fractional Burgers equations in one dimension is proposed. The method is based on L1 difference formula in time and ultra-weak discontinuous Galerkin formula in space. By carefully selecting interface numerical fluxes, we prove that the scheme is stable and it has optimal convergence order in the standard L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2$$\end{document} norm. Finally, two numerical examples are presented to verify our theoretical analysis.