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Combined triangular FV‐triangular FE method for nonlinear convection‐diffusion problems
Author(s) -
Bejček M.,
Feistauer M.,
Gallouet T.,
Hájek J.,
Herbin R.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200610332
Subject(s) - finite element method , finite volume method , polygon mesh , discretization , mathematics , mixed finite element method , nonlinear system , piecewise linear function , extended finite element method , finite volume method for one dimensional steady state diffusion , convection–diffusion equation , piecewise , mathematical analysis , diffusion , geometry , mechanics , physics , quantum mechanics , thermodynamics
The paper is concerned with the analysis of the combined finite element ‐ finite volume method for the solution of nonstationary nonlinear convection‐diffusion problems. Here a special version of this technique is analyzed, combining conforming piecewise linear triangular elements, used for the discretization of diffustion terms, with triangular finite volumes for the approximation of nonlinear convective terms. The finite volume and finite element meshes have to be of the same size, but their shape can be practically independent. In the paper, the error estimates of this method are proven under the assumptions that the finite element meshes are shape regular, the size of the finite element and finite volume meshes are equivalent and the exact solution is sufficiently regular. Theoretical analysis is accompanied by numerical experiments, showing the optimality of the derived error estimates.