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Morton, K. W.; Stynes, Martin; Süli, Endre

Analysis of a cell-vertex finite volume method for convection-diffusion problems. (English) Zbl 0885.65121

Math. Comput. 66, No. 220, 1389-1406 (1997).
This paper deals with the stability and the convergence of a cell-vertex finite volume method for linear elliptic convection-dominated diffusion equations in the plane. Using a combination of techniques from the theory of finite difference and finite element methods the authors prove that the scheme is stable in a mesh-dependent \(L_2\)-norm, uniformly as the diffusion coefficient tends to zero, and second-order convergent.
Reviewer: P.Chocholatý (Bratislava)

Cited in 19 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs

Keywords:

convection-diffusion problems; stability; error analysis; convergence; cell-vertex finite volume method; finite difference; finite element
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References:

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