Abstract

We propose and analyse a lumped surface finite element method for the numerical approximation of reaction–diffusion systems on stationary compact surfaces in R3. The proposed method preserves the invariant regions of the continuous problem under discretization and, in the special case of scalar equations, it preserves the maximum principle. On the application of a fully discrete scheme using the implicit–explicit Euler method in time, we prove that invariant regions of the continuous problem are preserved (i) at the spatially discrete level with no restriction on the meshsize and (ii) at the fully discrete level under a timestep restriction. We further prove optimal error bounds for the semidiscrete and fully discrete methods, that is, the convergence rates are quadratic in the meshsize and linear in the timestep. Numerical experiments are provided to support the theoretical findings.We provide examples in which, in the absence of lumping, the numerical solution violates the invariant region leading to blow-up.

Autore Pugliese

• Sgura Ivonne

Tutti gli autori

• M.Frittelli , A.Madzvamuse , I. Sgura , C. Venkataraman

Titolo volume/Rivista

IMA JOURNAL OF NUMERICAL ANALYSIS

Anno di pubblicazione

2017

ISSN

0272-4979

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

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Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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