Pointwise accuracy of a finite element method for nonlinear variational inequalities |
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Authors: | Ricardo H Nochetto |
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Institution: | (1) Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, 20742 College Park, MD, USA |
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Abstract: | Summary Consider the following quasilinear elliptic PDE, which is equivalent to a nonlinear variational inequality: –divF( u)+ (u) f. Here is a singular maximal monotone graph and the nonlinear differential operator is only assumed to be monotone; surfaces of prescribed mean curvature over obstacles may thus be viewed as relevant examples. The numerical approximation proposed in this paper consists of combining continuous piecewise linear finite elements with a preliminary regularization of . The resulting scheme is shown to be quasi-optimally accurate inL
. The underlying analysis makes use of both a topological technique and a sharpL
p
-duality argument.This work was partially supported by Consiglio Nazionale delle Ricerche of Italy while the author was in residence at the Istituto di Analisi Numerica del C.N.R. di Pavia![rdquo](/content/h2554545h7300u32/xxlarge8221.gif) |
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Keywords: | AMS(MOS): 65N15 65N30 35J85 35R35 CR: G1 8 |
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