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A finite element–finite volume discretization of convection‐diffusion‐reaction equations with nonhomogeneous mixedboundary conditions: Error estimates
Author(s) -
Deuring Paul
Publication year - 2016
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22064
Subject(s) - mathematics , finite element method , finite volume method , discretization , mathematical analysis , finite volume method for one dimensional steady state diffusion , piecewise linear function , partial differential equation , mechanics , numerical partial differential equations , physics , thermodynamics
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. TheL 2 ( H 1 ) ‐ and theL ∞ ( L 2 ) ‐error in the unsteady case and the H 1 ‐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