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Error estimate in a finite volume approximation of the partial asymptotic domain decomposition
Author(s) -
Panasenko Grigory,
Viallon MarieClaude
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2735
Subject(s) - domain decomposition methods , partial differential equation , domain (mathematical analysis) , dimension (graph theory) , mathematics , decomposition , set (abstract data type) , volume (thermodynamics) , finite volume method , mathematical analysis , mathematical optimization , computer science , finite element method , physics , combinatorics , mechanics , ecology , quantum mechanics , biology , thermodynamics , programming language
The method of asymptotic partial domain decomposition has been proposed for partial differential equations set in rod structures, depending on a small parameter. It reduces the dimension of the problem (or simplifies it in another way) in the main part of the domain keeping the initial formulation in the remaining part and prescribing the asymptotically precise conditions on the interface. This paper is devoted to the finite volume implementation of the method of asymptotic partial domain decomposition. We consider a model problem in a thin domain (its thickness is a small parameter). We obtain an error estimate, expressed in terms of the small parameter and the step of the mesh. Copyright © 2013 John Wiley & Sons, Ltd.