A non-symmetric coupling of the finite volume method and the boundary element method

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• 作者：Christoph Erath ; Günther Of ; Francisco-Javier Sayas
• 关键词：Mathematics Subject Classification65N08 ; 65N38 ; 65N12 ; 65N15
• 刊名：Numerische Mathematik
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：135
• 期：3
• 页码：895-922
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Appl.Mathematics/Comput
• 出版者：Springer Berlin Heidelberg
• ISSN：0945-3245
• 卷排序：135

文摘

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.