Numerical solution for an aggregation equation with degenerate diffusion

Roberto Carlos Cabrales, Juan Vicente Gutiérrez-Santacreu and José Rafael Rodríguez-Galván

Applied Mathematics and Computation, 2020, vol. 377, issue C

Abstract: A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a finite element method together with a mass lumping technique and an extra stabilizing term plus a semi–implicit Euler time integration. Then we carry out a rigorous passage to the limit as the spatial and temporal discretization parameters tend to zero, and show that the sequence of finite element approximations converges toward the unique weak solution of the model at hands. In doing so, nonnegativity is attained due to the stabilizing term and the acuteness on partitions of the computational domain, and hence a priori energy estimates of finite element approximations are established. As we deal with a nonlinear problem, some form of strong convergence is required. The key compactness result is obtained via an adaptation of a Riesz–Fréchet–Kolmogorov criterion by perturbation. A numerical example is also presented.

Keywords: Finite-element approximation; Aggregation equation; Nonlinear diffusion (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320301144
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301144

DOI: 10.1016/j.amc.2020.125145

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().