Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/3886

 Title: A posteriori error analysis for a reduced-basis approximation of two parabolic problems for tumour growth Other Titles: Анализ на апостериорната грешка за апроксимация с редуциран базис на две параболични задачи за растеж на тумори Authors: Rashkov, Peter Keywords: Department of Mathematical Modelling and Numerical Analysis Issue Date: Mar-2021 Publisher: Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences Series/Report no.: 2021;1 Abstract: This work presents a theoretical analysis for an a posteriori error estimate for a reduced-basis approximation of the solution for two parametrised parabolic problems. Their motivation is in mathematical oncology and they describe a) a model for brain tumour growth [14] and b) a model for phenotype evolution of a tumour based on [3, 13], with the free parameter being the therapeutic dose. The discretisation of the problems in space is realised by the finite element method, and the numerical integration uses a first-order IMEX scheme due to model b) being a integro-differental problem. The obtained a posteriori error estimate for the approximation error between the numerical solution and the reduced basis solution gives the opportunity for constructing a reduced basis for the solution manifold by combining a proper orthogonal decomposition of the temporal trajectories and a greedy algorithm over the parameter range, as has been done in the case of explicit or implicit integration of linear parabolic problems [8, 10]. Description: [Rashkov Peter; Рашков Петър] URI: http://hdl.handle.net/10525/3886 ISBN: 978-954-8986-51-1 (print)978-954-8986-58-8 (pdf) Appears in Collections: Preprints

Files in This Item:

File Description SizeFormat