Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion

By Bangti Jin, Raytcho D. Lazarov, Joeseph Pasciak, Zhi Zhou. 2013

135 citations recorded by the source corpus.

We consider the initial boundary value problem for the inhomogeneous time-fractional diu- sion 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 nite element methods. Almost optimal error estimates are obtained for right hand side data f(x; t)2 L 1 (0; T ; _ H q ()), 1 < q 1, for both semidiscrete schemes. For lumped mass method, the optimal L 2 ()-norm error estimate requires symmetric meshes. Finally, numerical experiments for one- and two-dimensional examples are presented to verify our theoretical results.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/44908ed750cea7e988c43c3c801eabd4b516f84c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. Martin Stynes
2. Raytcho D. Lazarov
3. Bangti Jin
4. Zhi Zhou
5. Chein-Shan Liu
6. William Rundell
7. Zhidong Zhang
8. Ting Wei

In Modeling and Simulation

1. Raytcho D. Lazarov
2. Zhi Zhou
3. Bangti Jin
4. Martin Stynes
5. William Rundell
6. Zhidong Zhang

In Numerical Analysis

1. Martin Stynes
2. Raytcho D. Lazarov
3. Bangti Jin
4. Zhi Zhou
5. Zhidong Zhang
6. William Rundell

Citations in the corpus

• Too much regularity may force too much uniqueness (2016, background): “Time-dependent problems with a fractional temporal derivative of order α ∈ (0, 1) ∪ (1, 2) have attracted much attention in recent years, since these problems arise in several models of physical processes—see the references in [5, 8, 11, 12, 14].”
• Time two-mesh algorithm combined with finite element method for time fractional water wave model (2018, unknown): “In view of the difficulty for solving the analytic solutions, increasing scholars have started to study some effective numerical methods for solving complex FPDEs with time, space and space-time fractional derivatives, which include finite difference methods [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1”
• Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, methodology): “The SG method was first developed and rigorously analyzed for nonsmooth data in [57, 58, 34] for problem (1.”