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dc.contributor.authorSevilla Cárdenas, Rubén
dc.contributor.authorGiacomini, Matteo
dc.contributor.authorHuerta, Antonio
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.identifier.citationSevilla, R., Giacomini, M., Huerta, A. A face-centred finite volume method for second-order elliptic problems. "International journal for numerical methods in engineering", 24 Agost 2018, vol. 115, núm. 8, p. 986-1014.
dc.description.abstractThis work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in 2D) to construct locally-conservative numerical schemes. The idea of the FCFV method stems from a hybridisable discontinuous Galerkin (HDG) formulation with constant degree of approximation, thus inheriting the convergence properties of the classical HDG. The resulting FCFV features a global problem in terms of a piecewise constant function defined on the faces of the mesh. The solution and its gradient in each element are then recovered by solving a set of independent element-by-element problems. The mathematical formulation of FCFV for Poisson and Stokes equation is derived and numerical evidence of optimal convergence in 2D and 3D is provided. Numerical examples are presented to illustrate the accuracy, efficiency and robustness of the proposed methodology. The results show that, contrary to other FV methods, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. In addition, the FCFV method shows its better performance, accuracy and robustness using simplicial elements, facilitating its application to problems involving complex geometries in 3D.
dc.format.extent29 p.
dc.publisherJohn Wiley & sons
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Equacions funcionals
dc.subject.lcshDifference equations, Partial--Numerical solutions
dc.subject.lcshDifferential equations, Elliptic
dc.subject.otherfinite volume method
dc.subject.otherhybridisable discontinuous Galerkin
dc.subject.otherlowest-order approximation
dc.titleA face-centred finite volume method for second-order elliptic problems
dc.subject.lemacEquacions diferencials parcials--solucions numèriques
dc.subject.lemacEquacions diferencials el·líptiques
dc.contributor.groupUniversitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems
dc.subject.amsClassificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorSevilla, R.; Giacomini, M.; Huerta, A.
local.citation.publicationNameInternational journal for numerical methods in engineering

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