2024/07/15 by Bartels, Sören, Gudi, Thirupathi, Kaltenbach, Alex
#35J20 #49J40 #49M29 #65N15 #65N30 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2407.10912
In this paper, on the basis of a (Fenchel) duality theory on the continuous level, we derive an a posteriori error identity for arbitrary conforming approximations of the primal formulation and the dual formulation of the scalar Signorini problem. In addition, on the basis of a (Fenchel) duality theory on the discrete level, we derive an a priori error identity that applies to the approximation of the primal formulation using the Crouzeix-Raviart element and to the approximation of the dual formulation using the Raviart-Thomas element, and leads to quasi-optimal error decay rates without imposing additional assumptions on the contact set and in arbitrary space dimensions.