Abstract
We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.
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This research was supported by the Grant Agency of Czech Republic under the contract No. 201/02/0595.
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Pultarova, I. The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions. Appl Math 50, 323–329 (2005). https://doi.org/10.1007/s10492-005-0020-4
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DOI: https://doi.org/10.1007/s10492-005-0020-4