An exponential integrator for finite volume discretization of a reaction-advection-diffusion equation

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• 作者：Antoine Tambue ; ^{antonio@aims.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Parabolic partial differential equation ; Finite volume method ; Exponential integrators ; Errors estimate
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：71
• 期：9
• 页码：1875-1897
• 全文大小：558 K

文摘

We consider the numerical approximation of a general second order semi-linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media. Using the finite volume with two-point flux approximation on regular mesh combined with exponential time differencing of order one (ETD1) for temporal discretization, we derive the L²$L^2$ estimate under the assumption that the non linear term is locally Lipschitz. Numerical simulations to sustain the theoretical results are provided.