A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A posteriori error estimators for mixed finite element methods in linear elasticity
Numerische Mathematik
On the stability of BDMS and PEERS elements
Numerische Mathematik
A Multigrid Preconditioner for the Mixed Formulation of Linear Plane Elasticity
SIAM Journal on Numerical Analysis
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A modified first-order system least squares formulation for linear elasticity, obtained by adding the antisymmetric displacement gradient in the test space, is analyzed. This approach leads to surprisingly small momentum balance error compared to standard least squares approaches. It is shown that the modified least squares formulation is well posed and its performance is illustrated by adaptive finite element computation based on using a closely related least squares functional as a posteriori error estimator. The results of our numerical computations show that, for the modified least squares approach, the momentum balance error converges at a much faster rate than the overall error. We prove that this is due to a strong connection of the stress approximation to that obtained from a mixed formulation based on the Hellinger-Reissner principle (with exact local momentum balance). The practical significance is that our proposed approach is almost momentum-conservative at a smaller number of degrees of freedom than mixed approximations with exact local momentum balance.