Numerical analysis to discontinuous Galerkin methods for the age structured population model of marine invertebrates |
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Authors: | Guanying Sun Dong Liang Wenqia Wang |
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Affiliation: | 1. School of Mathematics and System Sciences, Shandong University, Jinan 250100, China;2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3 |
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Abstract: | In this article we consider the age structured population growth model of marine invertebrates. The problem is a nonlinear coupled system of the age‐density distribution of sessile adults and the abundance of larvae. We propose the semidiscrete and fully‐discrete discontinuous Galerkin schemes to the nonlinear problem. The DG method is well suited to approximate the local behavior of the problem and to easily take the locally refined meshes with hanging nodes adaptively. The simple communication pattern between elements makes the DG method ideal for parallel computation. The global existence of the approximation solution is proved for the nonlinear approximation system by using the broken Sobolev spaces and the Schauder's fixed point theorem, and error estimates are obtained for both the semidiscrete scheme and the fully‐discrete scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 |
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Keywords: | age‐structure discontinuous Galerkin method error estimate, existence, fully‐discrete semidiscrete population growth |
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