2017/10/10 by Andreas Veeser, Veeser, Andreas, Pietro Zanotti +1
Computer Science · Engineering · #65N12 (Secondary) #65N30 (Primary) 65N15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1710.03452
openalex publication_date 2017/10/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We devise new variants of the following nonconforming finite element methods:\nDG methods of fixed arbitrary order for the Poisson problem, the\nCrouzeix-Raviart interior penalty method for linear elasticity, and the\nquadratic C0 interior penalty method for the biharmonic problem. Each\nvariant differs from the original method only in the discretization of the\nright-hand side. Before applying the load functional, a linear operator\ntransforms nonconforming discrete test functions into conforming functions such\nthat stability and consistency are improved. The new variants are thus\nquasi-optimal with respect to an extension of the energy norm. Furthermore,\ntheir quasi-optimality constants are uniformly bounded for shape regular meshes\nand tend to 1 as the penalty parameter increases.\n