A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Locally Conservative Fluxes for the Continuous Galerkin Method
SIAM Journal on Numerical Analysis
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We show how to postprocess the approximate displacement given by the continuous Galerkin method for compressible linearly elastic materials to obtain an optimally convergent approximate stress that renders the method locally conservative. The postprocessing is extremely efficient as it requires the inversion of a symmetric, positive definite matrix whose condition number is independent of the mesh size. Although the new stress is not symmetric, its asymmetry can be controlled by a small term which is of the same order as that of the error of the approximate stress itself. The continuous Galerkin method is thus competitive with mixed methods providing stresses with similar convergence properties.