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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:
65N06Finite difference methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
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 · doi:10.1137/0724050
[2]Hackbusch, W.: On the regularity of difference schemes. Arkiv för Matematik19 71–95 (1981). · Zbl 0462.65058 · doi:10.1007/BF02384470
[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 · doi:10.1007/BF02384298
[4]Hackbusch, W.: Multi-Grid Methods and Applications. Heidelberg: Springer 1985.
[5]Hackbusch, W.: Theorie und Numerik elliptischer Differentialgleichungen. Stuttgart: Teubner 1986. (English translation: to be published by Springer Heidelberg.)
[6]Heinrich, B.: Finite difference methods on irregular networks. A generalized approach to second order problems. ISNM vol. 82. Basel: Birkhäuser 1987.