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Error estimates for the combined h and p versions of the finite element method. (English) Zbl 0487.65058

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
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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References:
[1] Babuška, I., Kellogg, R.B., Pitkäranta, J.: Direct and inverse error estimates for finite elements with mesh refinement. Numer. Math.33, 447–471 (1979) · Zbl 0423.65057
[2] Babuška, I., Szabo, B.A., Katz, I.N.: Thep-version of the finite element method. Report WU/CCM-79/1, Center for Computational Mechanics, Washington University, SINUM (1981)
[3] Bergh, J., Löfstrom, J.: Interpolation spaces. Berlin-Heidelberg-New York: Springer 1976
[4] Ciarlet, P.: The finite element method for elliptic problems. Amsterdam: North-Holland 1978 · Zbl 0383.65058
[5] DeVore, R., Scherer, K.: Variable knot, variable degree spline approximation tox {\(\beta\)}. In: Quantitative approximation, Proceedings of the Bonn Conference. New York: Academic Press 1979
[6] Grisvard, P.: Boundary value problems in non-smooth domains. Lecture Notes 19, University of Maryland, 1980
[7] Kondrat’ev, V.A.: Boundary problems for elliptic equations with conical or angular points. Trans. Moscow Math Soc.16, 227–313 (1967) · Zbl 0194.13405
[8] Stein, E.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970 · Zbl 0207.13501
[9] Widlund, O.: On best error bounds for approximation by piecewise polynomial functions. Numer. Math.27, 327–338, 1977 · Zbl 0331.41010
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