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Comparison of Galerkin and control volume finite element for advection–diffusion problems
Author(s) -
Martinez M. J.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1060
Subject(s) - upwind scheme , finite element method , control volume , finite volume method , volume of fluid method , advection , mathematics , discontinuous galerkin method , context (archaeology) , numerical diffusion , unstructured grid , convection–diffusion equation , conservation of mass , grid , mathematical optimization , mechanics , mathematical analysis , geometry , engineering , flow (mathematics) , physics , geology , thermodynamics , paleontology , structural engineering , discretization
The control volume finite element method (CVFEM) was developed to combine the local numerical conservation property of control volume methods with the unstructured grid and generality of finite element methods (FEMs). Most implementations of CVFEM include mass‐lumping and upwinding techniques typical of control volume schemes. In this work we compare, via numerical error analysis, CVFEM and FEM utilizing consistent and lumped mass implementations, and stabilized Petrov–Galerkin streamline upwind schemes in the context of advection–diffusion processes. For this type of problem, we find no apparent advantage to the local numerical conservation aspect of CVFEM as compared to FEM. The stabilized schemes improve accuracy and degree of positivity on coarse grids, and also reduce iteration counts for advection‐dominated problems. Published in 2005 by John Wiley & Sons, Ltd.