Stabilized Finite Element Methods for Predator-Prey Systems

Year 2019, Volume: 19 Issue: 3, 653 - 661, 31.12.2019

Ali Şendur

https://doi.org/10.35414/akufemubid.597506

Abstract

A numerical method that will improve and
produce effective results for solving mathematical model for the system of
predator-prey interactions which is defined by convection-diffusion-reaction
problem is studied herein. We consider the Pseudo Residual-free Bubble (PRFB)
method which is based on augmenting the finite element space by a set
appropriate functions for the space discretization. The method is applied on
different test problems and the numerical solutions are in good agreement with
the result available in literature. The numerical results depict that the
algorithm is efficient and feasible

Keywords

Predator-prey systems; Convection-diffusion-reaction; Stabilized finite element method; Multiscale Methods

Av-Avcı Problemleri için Kararlı Sonlu Eleman Yöntemleri Üzerine Bir Not

Abstract

Bu
çalışmada, konveksiyon-difüzyon-reaksiyon problemleri ile modellenebilen
av-avcı denklem sistemlerinin simülasyonunda kullanılan sayısal çözüm
tekniklerini iyileştirecek ve daha etkin sonuçlar üretecek sayısal bir yöntem
önerilmiştir. Uzay ayrıklaştırması için, sonlu elemanlar metodunu uygularken
seçilen polinom baz fonksiyonlarına ilaveten fonksiyon uzayının özel tip
fonksiyonlarla (residual-free bubbles) zenginleştirilmesine dayanan Pseudo
Residual-free Bubble (PRFB) yöntemi kullanılmıştır. Söz konusu yöntem, çeşitli
test örneklerine uygulanmış olup elde edilen sayısal çözümlerin, literatürde
mevcut olan sonuçlar ile iyi bir uyum içinde olduğu gözlemlenmiştir. Sayısal
sonuçlar, önerilen yöntemin verimli ve uygulanabilir olduğunu göstermektedir.

Keywords

Av-avcı denklem sistemleri, Konveksiyon-difüzyon-reaksiyon, Kararlı Sonlu Eleman Yöntemi, Çok-ölçekli Yöntemler

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