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Finite element methods for nonlinear elliptic systems of second order
Author(s) -
Dobrowolski Manfred,
Rannacher Rolf
Publication year - 1980
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19800940112
Subject(s) - mathematics , finite element method , nonlinear system , argument (complex analysis) , order (exchange) , displacement (psychology) , element (criminal law) , deformation (meteorology) , mathematical analysis , calculus (dental) , structural engineering , law , medicine , psychology , biochemistry , chemistry , physics , finance , dentistry , quantum mechanics , meteorology , political science , engineering , economics , psychotherapist
This paper deals with the finite element displacement method for approximating isolated solutions of general quasilinear elliptic systems. Under minimal assumptions on the structure of the continuous problems it is shown that the discrete analogues also have locally unique solutions which converge with quasi‐optimal rates in L 2 and L ∞. The essential tools of the proof are a deformation argument and a technique using weighted L 2 ‐norms.