Summary
The stability ofL 2-projection into many standard finite element spaces as a map intoL q, 1≦q≦∞, is demonstrated. TheL 2-projection ofu∈L q is shown to be a quasi-optimal approximation ofu inL q.
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References
Ciarlet, P. G.: Sur l'élément de Clough et Toucher. To appear
Ciarlet, P. G., Raviart, P. A.: Interpolation theory over curved elements, with applications to finite element methods. Computer Methods in Applied Mechanics and Engineering.1, 217–249 (1972)
Ciarlet, P. G., Raviart, P. A.: General Lagrange and Hermite interpolation inR n with applications to finite element methods. Arch. Rational Mech. Anal.46, 177–199 (1972)
Douglas, J., Jr., Dupont, T., Wahlbin, L.: OptimalL ∞ error estimates for Galerkin approximations to solutions of two point boundary value problems. To appear in: Mathematics of Computation, April 1975.
Thorin, G. O.: Convexity theorems generalizing those of M. Riesz and Hadamard with some applications. Medd. Lunds Univ. Matem. Sem.9 (1948)
Zienkiewicz, O. C.: The finite element method in engineering scince. London: McGraw-Hill 1971
Zygmund, A.: Trigonometric series. New York: Cambridge University Press 1959
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Douglas, J., Dupont, T. & Wahlbin, L. The stability inL q of theL 2-projection into finite element function spaces. Numer. Math. 23, 193–197 (1974). https://doi.org/10.1007/BF01400302
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DOI: https://doi.org/10.1007/BF01400302