TY - JOUR
T1 - A mixed finite element method for nonlinear elasticity
T2 - Two-fold saddle point approach and a-posteriori error estimate
AU - Barrientos, Mauricio A.
AU - Gatics, Gabriel N.
AU - Stephan, Ernst P.
PY - 2002/4
Y1 - 2002/4
N2 - We extend the applicability of stable mixed finite elements for linear plane elasticity, such as PEERS, to a mixed variational formulation of hyperelasticity. The present approach is based on the introduction of the strain tensor as a further unknown, which yields a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solution for the continuous and discrete schemes, and derive the usual Cea estimate for the associated error. Finally, a reliable a-posteriori error estimate, based on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given.
AB - We extend the applicability of stable mixed finite elements for linear plane elasticity, such as PEERS, to a mixed variational formulation of hyperelasticity. The present approach is based on the introduction of the strain tensor as a further unknown, which yields a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solution for the continuous and discrete schemes, and derive the usual Cea estimate for the associated error. Finally, a reliable a-posteriori error estimate, based on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given.
UR - http://www.scopus.com/inward/record.url?scp=0036013090&partnerID=8YFLogxK
U2 - 10.1007/s002110100337
DO - 10.1007/s002110100337
M3 - Article
AN - SCOPUS:0036013090
SN - 0029-599X
VL - 91
SP - 197
EP - 222
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 2
ER -