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Hybrid finite element methods for the Signorini problem. (English) Zbl 1023.74043
Summary: We study three mixed linear finite element methods for numerical simulation of two-dimensional Signorini problem. Applying Falk’s lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these finite elements provide optimal results under reasonable regularity assumptions on Signorini solution, and the numerical investigation shows that the third method also provides optimal accuracy.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
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