A mixed formulation for frictional contact problems prone to Newton like solution methods
Computer Methods in Applied Mechanics and Engineering
Quadratic finite element approximation of the Signorini problem
Mathematics of Computation
Positivity preserving finite element approximation
Mathematics of Computation
Quadratic finite element methods for unilateral contact problems
Applied Numerical Mathematics
A Primal-Dual Active Set Algorithm for Three-Dimensional Contact Problems with Coulomb Friction
SIAM Journal on Scientific Computing
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Mortar methods with curved interfaces
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Optimal a priori estimates for higher order finite elements for elliptic interface problems
Applied Numerical Mathematics
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In this paper, a variationally consistent contact formulation is considered and we provide an abstract framework for the a priori error analysis in the special case of frictionless contact and small deformations. Special emphasis is put on quadratic mortar finite element methods. It is shown that under quite weak assumptions on the Lagrange multiplier space $${\mathcal{O} (h^{t-1}), 2 , a priori results in the H 1-norm for the error in the displacement and in the H 驴1/2-norm for the error in the surface traction can be established provided that the solution is regular enough. We discuss several choices of Lagrange multipliers ranging from the standard lowest order conforming finite elements to locally defined biorthogonal basis functions. The crucial property for the analysis is that the basis functions have a local positive mean value. Numerical results are exemplarily presented for one particular choice of biorthogonal (i.e. dual) basis functions and also comprise the case of finite deformation contact.