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On first and second order box schemes. (English) Zbl 0649.65052
The box method for discretizing elliptic boundary value problems is discussed. Error estimates of first and second order between the Galerkin solution and the box method solution are proved. A proposal for a new second order box-like scheme is made.
Reviewer: W.Hackbusch

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
Full Text: DOI
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[5] Hackbusch, W.: Theorie und Numerik elliptischer Differentialgleichungen. Stuttgart: Teubner 1986. (English translation: to be published by Springer Heidelberg.) · Zbl 0609.65065
[6] Heinrich, B.: Finite difference methods on irregular networks. A generalized approach to second order problems. ISNM vol. 82. Basel: Birkhäuser 1987. · Zbl 0623.65096
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