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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]
ISBN: 978-954-8986-51-1 (print)
978-954-8986-58-8 (pdf)
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