document: In this work, we have developed a simple numerical scheme based on the Galerkin finite element method for a multi-term time fractional diffusion equation which involves multiple Caputo fractional derivatives in time. A complete error analysis of the space semidiscrete Galerkin scheme is provided. The theory covers the practically very important case of nonsmooth initial data and right hand side. The analysis relies essentially on some new regularity results of the multi-term time fractional diffusion equation. Further, we have developed a fully discrete scheme based on a finite difference discretization of the Caputo fractional derivatives. The stability and error estimate of the fully discrete scheme were established, provided that the solution is smooth. The extensive numerical experiments in one- and two-dimension fully confirmed our convergence analysis: the empirical convergence rates agree well with the theoretical predictions for both smooth and nonsmooth data.
doc_bio_tags: O O O O O O O O B I O O O B I I I O O O O O O O O O B I I I I I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B I I O O O B I I I I I I I O O O O O O O B I I O O O O O O O O O O B I O O O O O O O O O O B I I O O O O O O O O O O O O