Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview

DOI10.1016/J.CMA.2018.12.011zbMATH Open1440.65138arXiv1805.11309OpenAlexW2806752574WikidataQ128736066 ScholiaQ128736066MaRDI QIDQ1986890

Author name not available (Why is that?)

Publication date: 9 April 2020

Published in: (Search for Journal in Brave)

Abstract: Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $alphain(0,1)$ in time, due to their many successful applications in engineering, physics, biology and finance. Thus, it is of paramount importance to develop and to analyze efficient and accurate numerical methods for reliably simulating such models, and the literature on the topic is vast and fast growing. The present paper gives a concise overview on numerical schemes for the subdiffusion model with nonsmooth problem data, which are important for the numerical analysis of many problems arising in optimal control, inverse problems and stochastic analysis. We focus on the following aspects of the subdiffusion model: regularity theory, Galerkin finite element discretization in space, time-stepping schemes (including convolution quadrature and L1 type schemes), and space-time variational formulations, and compare the results with that for standard parabolic problems. Further, these aspects are showcased with illustrative numerical experiments and complemented with perspectives and pointers to relevant literature.

Full work available at URL: https://arxiv.org/abs/1805.11309

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1986890)