Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions
KAUST Grant NumberKUS-C1-016-04
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Abstract© 2014 Elsevier Inc. In this paper the interpolation inequality of Szepessy [12, Lemma 4.2] is revisited. The lower bound in the above reference is proven to be proportional to p<sup>-2</sup>, where p is a polynomial degree, that goes fast to zero as p increases. We prove that the lower bound is proportional to ln<sup>2</sup> p which is an increasing function. Moreover, we prove that this estimate is sharp.
CitationMuhamadiev È, Nazarov M (2015) Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions. Journal of Mathematical Analysis and Applications 423: 940–955. Available: http://dx.doi.org/10.1016/j.jmaa.2014.10.027.
SponsorsThe second author is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).