Error Estimates for Barycentric Finite Volumes Combined with Nonconforming Finite Elements Applied to Nonlinear Convection-Diffusion Problems

The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangul...

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Bibliographic Details
Published inApplications of mathematics (Prague) Vol. 47; no. 4; pp. 301 - 340
Main Authors Dolejsi, Vit, Feistauer, Miloslav, Felcman, Jiri, Klikova, Alice
Format Journal Article
LanguageEnglish
Published Prague Springer Nature B.V 01.08.2002
Subjects
Applications of mathematics
Derivation
Errors
Estimates
Exact solutions
Finite element analysis
Finite element method
Mathematical analysis
Mathematical models
Nonlinearity
Studies
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ISSN0862-7940
1572-9109
DOI10.1023/A:1021701705932

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Summary:The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the L^sup 2^(L^sup 2^) and L^sup 2^(H^sup 1^) error estimates are established. At the end of the paper, some computational results are presented demonstrating the application of the method to the solution of viscous gas flow.[PUBLICATION ABSTRACT]
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ISSN:0862-7940
1572-9109
DOI:10.1023/A:1021701705932