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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

MSC:

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
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References:

[1] Bank, R., Rose, D. J.: Some error estimates for the box method. SIAM J. Numer. Anal.24, 777–787 (1987). · Zbl 0634.65105
[2] Hackbusch, W.: On the regularity of difference schemes. Arkiv för Matematik19 71–95 (1981). · Zbl 0462.65058
[3] Hackbusch, W.: On the regularity of difference schemes–part II: regularity estimates for linear and nonlinear problems. Arkiv för Matematik21 3–28 (1983). · Zbl 0535.65071
[4] Hackbusch, W.: Multi-Grid Methods and Applications. Heidelberg: Springer 1985. · Zbl 0595.65106
[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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