Document Zbl 0423.65057

Babuška, Ivo; Kellogg, R. B.; Pitkäranta, J.

Direct and inverse error estimates for finite elements with mesh refinements. (English) Zbl 0423.65057

Numer. Math. 33, 447-471 (1979).

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MSC:

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

Keywords:

finite element method; second order elliptic boundary value problem; weighted Besov spaces; optimal error estimates

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References:

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[2]	Babuška, I., Kellogg, R.B.: Nonuniform error for the finite element method SIAM J. Numer. Anal.12, 868–875 (1975) · Zbl 0339.65062 · doi:10.1137/0712064
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[4]	Bergh, J., Löfstrom, J.: Interpolation Spaces. Berlin, Heidelberg, New York: Springer: 1976
[5]	Ciarlet, P.: The finite element method for elliptic problems. Amsterdam North-Holland: 1978 · Zbl 0383.65058
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[8]	Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities, 2nd ed., Cambridge: Cambridge Univ. Press 1952
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[10]	Raugel, G.: Résolution numérique de problemes elliptiques dans des domains avec coins. Thesis, University of Rennes, 1978
[11]	Schatz, A., Wahlbin, L.: Maximum norm estimates in the finite element method on plane polygonal domains, Part 1. Math of Comp.32, 73–109 (1978) · Zbl 0382.65058
[12]	Schatz, A., Wahlbin, L.: Maximum norm estimates in the finite element method on plane polygonal domains, Part II. Math. Comput.33, 465–492 (1979) · Zbl 0417.65053
[13]	Stein, E.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press, 1970 · Zbl 0207.13501
[14]	Wait, R., Mitchell, A.R.: Corner singularities in elliptic problems by finite element methods. J. Comp. Physics8, 45–52 (1971) · Zbl 0224.65030 · doi:10.1016/0021-9991(71)90033-7
[15]	Whiteman, J.R., Barnhill, R.L.: Finite element methods for elliptic boundary value problems. Proc. Equadiff 3, Czechoslovak Conf. on Diff. Eqns., Brno, Czechoslovakia · Zbl 0284.65087
[16]	Widlund, O.: On best error bounds for approximation by piecewise polynomial functions. Numer. Math.27, 327–338 (1977) · Zbl 0331.41010 · doi:10.1007/BF01396181

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