 
Summary: Numer.Math. 45, 122(1984) Numerische
Mathematik
9 SpringerVerlag1984
A Family of Higher Order Mixed Finite Element Methods
for Plane Elasticity
Douglas N. Arnold .1, Jim Douglas, Jr. 2, and Chaitan P. Gupta 3
Departmentof Mathematics,Universityof Maryland,CollegePark. MD 20742,USA
2 Departmentof Mathematics,Universityof Chicago,Chicago,IL 60637,USA
3Departmentof Mathematics,Northern Illinois University,DeKalb, IL 60115, USA
Summary. The Dirichlet problem for the equations of plane elasticity is
approximated by a mixed finite element method using a new family of
composite finite elements having properties analogous to those possessed
by the RaviartThomas mixed finite elements for a scalar, secondorder
elliptic equation. Estimates of optimal order and minimal regularity are
derived for the errors in the displacement vector and the stress tensor in
L2(f2), and optimal order negative norm estimates are obtained in H=(g2)' for
a range of s depending on the index of the finite element space. An optimal
order estimate in L~176 for the displacement error is given. Also, a quasiop
timal estimate is derived in an appropriate space. All estimates are valid
uniformly with respect to the compressibility and apply in the incom
