2025/05/27 by Tom Gustafsson, Gustafsson, Tom, Rolf Stenberg +1 · 1 citation
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2505.21776
openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two methods for treating elastic contact problems with the finite element method; the penalty method and Nitsche's method. For the penalty method we discuss how the penalty parameter should be chosen. Both the theoretical analysis and numerical examples show that an optimal convergence rate cannot be achieved. The method is contrasted to that of Nitsche which is optimally convergent. We also give the derivation of Nitsche's method by a very simple consistency correction of the penalty method.