Analysis of a combined barycentric finite volume—nonconforming finite element method for nonlinear convection-diffusion problems. (English) Zbl 0942.76035

The paper presents numerical analysis of a nonlinear convection-diffusion problem in a two-dimensional polygonal domain. A combined barycentric finite volume and nonconforming triangular piecewise-linear finite element method is used for the discretization of nonlinear convective terms and linear diffusion terms, respectively, while the time discretization is implicit. Under some standard assumptions, the authors prove the discrete maximum principle, and establish stability and consistency of the discretization. Some a priori error estimates allow to prove the convergence theorem. In the introduction, the authors mention selected applications of the approach to problems of fluid dynamics.
Reviewer: K.Segeth (Praha)


76M10 Finite element methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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