ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

A mimetic discretization method for linear elasticity

Beirão Da Veiga, Lourenco

Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy. lourenco.beirao@unimi.it

Abstract

A Mimetic Discretization method for the linear elasticity problem in mixed weakly symmetric form is developed. The scheme is shown to converge linearly in the mesh size, independently of the incompressibility parameter λ, provided the discrete scalar product satisfies two given conditions. Finally, a family of algebraic scalar products which respect the above conditions is detailed.

(Received October 31 2008)

(Revised July 3 2009)

(Online publication January 27 2010)

Key Words:

  • Mimetic finite difference methods;
  • linear elasticity;
  • finite element methods;
  • mixed formulation

Mathematics Subject Classification:

  • 65N30;
  • 65N12;
  • 74B05
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