Details

Autor(en) / Beteiligte

• Huang, Chaobao
• Chen, Hu
• An, Na

Titel

β-Robust Superconvergent Analysis of a Finite Element Method for the Distributed Order Time-Fractional Diffusion Equation

Ist Teil von

• Journal of scientific computing, 2022, Vol.90 (1), p.44, Article 44

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• A distributed order time fractional diffusion equation whose solution has a weak singularity near the initial time t = 0 is considered. The numerical method of the paper uses the well-known L1 scheme on a graded mesh to discretize the time Caputo fractional derivative and a standard finite element method in space. A β -robust discrete fractional Grönwall inequality is investigated. By this inequality, the β -robust optimal-rate convergence and a superconvergence bound ‖ ∇ R h u n - ∇ u h n ‖ are proved. This superconvergence bound is also used to show that a simple postprocessing of the computed solution will yield a higher order of convergence in the spatial direction. The final convergence result reveals the optimal grading that one should use for the temporal graded mesh. Numerical results show that our analysis is sharp.