An abstract framework for a priori estimates for contact problems in 3D with quadratic finite elements
Dokumenttyp:
Zeitschriftenaufsatz
Autor(en):
Wohlmuth, B.I.; Popp, A.; Gee, M.W.; Wall, W.A
Abstract:
In this paper, a variationally consistent contact
formulation including Coulomb friction 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 O(h^{t-1}), 2 < t < 5/2 , a priori results
in the H^1-norm for the error in the displacement and
in the H^{−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.
Stichworte:
mortar finite element methods; Lagrange multipliers; contact problems; a priori error analysis