Least-squares methods for linear elasticity based on a discrete minus one inner product Academic Article uri icon

abstract

  • The purpose of this paper is to develop and analyze least-squares approximations for elasticity problems. The major advantage of the least-squares formulation is that it does not require that the classical Ladyzhenskaya Babǔska-Brezzi (LBB) condition be satisfied. By employing least-squares functionals which involve a discrete inner product which is related to the inner product in H-I(Ω) (the Sobolev space of order minus one on Ω) we develop a finite element method which is unconditionally stable for problems with traction type of boundary conditions and for almost and incompressible elastic media. The use of such inner products (applied to second-order problems) was proposed in an earlier paper by Bramble, Lazarov and Pasciak [Math. Comp. 66 (1997) 935]. © 2001 Elsevier Science B.V. All rights reserved.

author list (cited authors)

  • Bramble, J. H., Lazarov, R. D., & Pasciak, J. E.

citation count

  • 15

complete list of authors

  • Bramble, James H||Lazarov, Raytcho D||Pasciak, Joseph E

publication date

  • December 2001