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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 1-21, 2022/10/25
We consider an elliptic boundary value problem on a domain with regularboundary and discretize it with isoparametric finite elements of order$k\geq1$.We show optimal order of convergence of the isoparametric finiteelement solution in the $W^{1,\infty}$-norm. As an intermediate step,we derive stability and convergence estimates of optimal order $k$ fora (generalized) Ritz map.
Keywords: elliptic boundary value problem, nonconforming space discretization, isoparametric finite elements, Ritz map, maximum norm error estimates, a priori error estimates, weighted norms