2017/07/25 by Beiping Duan, Duan, Beiping, Bangti Jin +7
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1707.08057
openalex publication_date 2017/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order α∈(0,1) in time and zero initial data. We derive a proper weak formulation involving different solution and test spaces and show the inf-sup condition for the bilinear form and thus its well-posedness. Further, we develop a novel finite element formulation, show the well-posedness of the discrete problem, and establish error bounds in both energy and L2 norms for the finite element solution. In the proof of the discrete inf-sup condition, a certain nonstandard L2 stability property of the L2 projection operator plays a key role. We provide extensive numerical examples to verify the convergence of the method.