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Zbl 1067.65092
Chatzipantelidis, P.; Lazarov, R.D.; Thomée, V.
Error estimates for a finite volume element method for parabolic equations in convex polygonal domains. (English)
[J] Numer. Methods Partial Differ. Equations 20, No. 5, 650-674 (2004). ISSN 0749-159X; ISSN 1098-2426/e

A parabolic problem in a bounded, convex polygonal domain in the plane is considered. \par Some details about error estimates for the finite element method are given. The next section deals with the finite volume method. Section 4 is devoted to an alternative way to obtain an $\cal{O} (h^2)$ error bound for the finite volume method presented before. In Section 5, the technique of Section 4 is applied to derive error bounds in $H^1$ and $L^{\infty}$ norms. In Section 6 a lumped mass finite volume method is considered. In this case, the method loses the property of being locally conservative. Finally, the authors show that the proposed approach also applies to fully discrete schemes.
[Ruxandra Stavre (Bucureşti)]

MSC 2000:: *65M15 Error bounds (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
65M20 Method of lines (IVP of PDE)
35K15 Second order parabolic equations, initial value problems
65M60 Finite numerical methods (IVP of PDE)

Keywords: finite volume element method; parabolic equation; error estimates; elliptic projection

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