Author:
Christof Constantin,Haubner Christof
Abstract
AbstractThis paper is concerned with error estimates for the piecewise linear finite element approximation of the two-dimensional scalar Signorini problem on a convex polygonal domain $$\varOmega $$
Ω
. Using a Céa-type lemma, a supercloseness result, and a non-standard duality argument, we prove $$W^{1,p}(\varOmega )$$
W
1
,
p
(
Ω
)
-, $$L^\infty (\varOmega )$$
L
∞
(
Ω
)
-, $$W^{1,\infty }(\varOmega )$$
W
1
,
∞
(
Ω
)
-, and $$H^{1/2}(\partial \varOmega )$$
H
1
/
2
(
∂
Ω
)
-error estimates under reasonable assumptions on the regularity of the exact solution and $$L^p(\varOmega )$$
L
p
(
Ω
)
-error estimates under comparatively mild assumptions on the involved contact sets. The obtained orders of convergence turn out to be optimal for problems with essentially bounded right-hand sides. Our results are accompanied by numerical experiments which confirm the theoretical findings.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
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