- Title
- A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems
- Creator
- Lamichhane, Bishnu P.; Stephan, Ernst P.
- Relation
- Numerical Methods for Partial Differential Equations Vol. 28, Issue 4, p. 1336-1353
- Publisher Link
- http://dx.doi.org/10.1002/num.20683
- Publisher
- John Wiley & Sons
- Resource Type
- journal article
- Date
- 2011
- Description
- We present a symmetric version of the nonsymmetric mixed finite element method presented in (Lamichhane, ANZIAM J 50 (2008), C324–C338) for nearly incompressible elasticity. The displacement–pressure formulation of linear elasticity is discretized using a Petrov–Galerkin discretization for the pressure equation in (Lamichhane, ANZIAM J 50 (2008), C324–C338) leading to a non-symmetric saddle point problem. A new three-field formulation is introduced to obtain a symmetric saddle point problem which allows us to use a biorthogonal system. Working with a biorthogonal system, we can statically condense out all auxiliary variables from the saddle point problem arriving at a symmetric and positive-definite system based only on the displacement. We also derive a residual based error estimator for the mixed formulation of the problem.
- Subject
- mixed finite elements; symmetric system; Petrov Galerkin discretization; biorthogonal system
- Identifier
- http://hdl.handle.net/1959.13/940096
- Identifier
- uon:12946
- Identifier
- ISSN:0749-159X
- Language
- eng
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