Variational Formulation and A Priori Estimates for the Galerkin Method for a Fractional Diffusion Equation

Authors

DOI:

https://doi.org/10.5540/tcam.2022.023.04.00673

Keywords:

Galerkin method, fractional diffusion equation, {\it a priori} estimates.

Abstract

In this work we obtain a variational formulation and {\it a priori} estimates for approximate solutions of a problem involving fractional diffusion equations.

References

P. Biler, T. Funaki & W.A. Woyczynski. Fractal Burgers equations. Journal of Differential Equations, 148(1) (1998), 9–46.

M.P. Bonkile, A. Awasthi, C. Lakshmi, V. Mukundan & V. Aswin. A systematic literature review of Burgers’ equation with recent advances. Pramana, 90(6) (2018), 1–21.

L. Djilali & A. Rougirel. Galerkin method for time fractional diffusion equations. Journal of Elliptic and Parabolic Equations, 4(2) (2018), 349–368.

L.C. Evans. Partial Differential Equations. Graduate Studies in Mathematics, 19(4) (1998), 7.

J. Kemppainen, J. Siljander, V. Vergara & R. Zacher. Decay estimates for time-fractional and other non-local in time subdiffusion equations in Rd. Mathematische Annalen, 366(3) (2016), 941–979.

A.A. Kilbas, H.M. Srivastava & J.J. Trujillo. “Theory and Applications of Fractional Differential Equations”, volume 204. Elsevier (2006).

A. Lischke, G. Pang, M. Gulian, F. Song, C. Glusa, X. Zheng, Z. Mao, W. Cai, M.M. Meerschaert, M. Ainsworth et al. What is the fractional Laplacian? A comparative review with new results. Journal of Computational Physics, 404 (2020), 109009.

R. Metzler & J. Klafter. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339(1) (2000), 1–77.

W.R. Schneider &W.Wyss. Fractional diffusion and wave equations. Journal of Mathematical Physics, 30(1) (1989), 134–144.

Downloads

Published

2022-11-08

How to Cite

Lima, M. E. de S., Oliveira, E. C. de, & Viana, A. da C. (2022). Variational Formulation and A Priori Estimates for the Galerkin Method for a Fractional Diffusion Equation. Trends in Computational and Applied Mathematics, 23(4), 673–682. https://doi.org/10.5540/tcam.2022.023.04.00673

Issue

Section

Original Article