A finite element–finite volume discretization of convection‐diffusion‐reaction equations with nonhomogeneous mixedboundary conditions: Error estimates |
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Authors: | Paul Deuring |
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Affiliation: | Univ. Littoral C?te d'Opale, Laboratoire de mathématiques pures et appliquées Joseph Liouville, Calais, France |
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Abstract: | We consider a time‐dependent and a steady linear convection‐diffusion‐reaction equation whose coefficients are nonconstant. Boundary conditions are mixed (Dirichlet and Robin–Neumann) and nonhomogeneous. Both the unsteady and the steady problem are approximately solved by a combined finite element–finite volume method: the diffusion term is discretized by Crouzeix–Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. The ‐ and the ‐error in the unsteady case and the H1‐error in the steady one are estimated against the data, in such a way that no parameter enters exponentially into the constants involved. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1591–1621, 2016 |
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Keywords: | convection‐diffusion equation combined finite element– finite volume method Crouzeix– Raviart finite elements barycentric finite volumes upwind method error estimates |
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