A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Error estimators for nonconforming finite element approximations of the Stokes problem
Mathematics of Computation
A posteriori error estimate for the mixed finite element method
Mathematics of Computation
SIAM Journal on Scientific Computing
A unifying theory of a posteriori finite element error control
Numerische Mathematik
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
SIAM Journal on Numerical Analysis
A Multigrid Method for the Pseudostress Formulation of Stokes Problems
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
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The pseudostress-velocity formulation of the stationary Stokes problem allows a Raviart-Thomas mixed finite element formulation with quasi-optimal convergence and some superconvergent reconstruction of the velocity. This local postprocessing gives rise to some averaging a posteriori error estimator with explicit constants for reliable error control. Standard residual-based explicit a posteriori error estimation is shown to be reliable and efficient and motivates adaptive mesh-refining algorithms. Numerical experiments confirm our theoretical findings and illustrate the accuracy of the guaranteed upper error bounds even with reduced regularity.