Error Analysis of Semidiscrete Finite Element Methods for Inhomogeneous Time-Fractional Diffusion

2013/07/03 by Bangti Jin, Raytcho Lazarov, Jin, Bangti +5
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.1307.1068

openalex publication_date 2013/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the initial boundary value problem for the inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and a nonsmooth right hand side data in a bounded convex polyhedral domain. We analyze two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right hand side data f(x,t)∈ L^∞(0,T; H^q(Ω)), -1< q ≤ 1, for both semidiscrete schemes. For lumped mass method, the optimal L²(Ω)-norm error estimate requires symmetric meshes. Finally, numerical experiments for one- and two-dimensional examples are presented to verify our theoretical results.

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