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A second-order face-centred finite volume method for elliptic problems

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Vieira, Luan M.
Giacomini, MatteoMés informacióMés informacióMés informació
Sevilla Cárdenas, RubénMés informació
Huerta, AntonioMés informacióMés informacióMés informació
Document typeArticle
Defense date2020-01-01
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
ProjectAdMoRe - Empowered decision-making in simulation-based engineering: Advanced Model Reduction for real-time, inverse and optimization in industrial problems (EC-H2020-675919)
ASIMILACION DE DATOS PARA UNA SIMULACION INGENIERIL CREIBLE (AEI-DPI2017-85139-C2-2-R)
Abstract
A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving an element-by-element problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented.
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© 2020 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
CitationVieira, L. M. [et al.]. A second-order face-centred finite volume method for elliptic problems. "Computer methods in applied mechanics and engineering", 1 Gener 2020, vol. 358, p. 112655:1-112655:23. 
URIhttp://hdl.handle.net/2117/178278
DOI10.1016/j.cma.2019.112655
ISSN0045-7825
Publisher versionhttps://www.sciencedirect.com/science/article/pii/S0045782519305407?via%3Dihub
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