A hybrid mass transport finite element method for Keller--Segel type systems

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Title: A hybrid mass transport finite element method for Keller--Segel type systems
Authors: Carrillo de la Plata, JA
Kolbe, N
Lukácová-Medvidová, M
Item Type: Journal Article
Abstract: We propose a new splitting scheme for general reaction–taxis–diffusion systems in one spatial dimension capable to deal with simultaneous concentrated and diffusive regions as well as travelling waves and merging phenomena. The splitting scheme is based on a mass transport strategy for the cell density coupled with classical finite element approximations for the rest of the system. The built-in mass adaption of the scheme allows for an excellent performance even with respect to dedicated mesh-adapted AMR schemes in original variables.
Issue Date: 1-Sep-2019
Date of Acceptance: 21-Jun-2019
URI: http://hdl.handle.net/10044/1/71662
DOI: 10.1007/s10915-019-00997-0
ISSN: 0885-7474
Publisher: Springer (part of Springer Nature)
Start Page: 1777
End Page: 1804
Journal / Book Title: Journal of Scientific Computing
Volume: 80
Issue: 3
Copyright Statement: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Mass transport schemes
Reaction-aggregation-diffusion systems
Splitting schemes
Tumor invasion models
NONLINEAR CONTINUITY EQUATIONS
CANCER STEM-CELLS
NUMERICAL-SIMULATION
LAGRANGIAN SCHEME
CHEMOTAXIS
INVASION
MODEL
IDENTIFICATION
CONVERGENCE
Applied Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Publication Status: Published
Online Publication Date: 2019-06-27
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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