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
Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
SIAM Journal on Numerical Analysis
Poincaré-Friedrichs Inequalities for Piecewise H1 Functions
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A posteriori error estimators for locally conservative methods of nonlinear elliptic problems
Applied Numerical Mathematics
A unifying theory of a posteriori error control for nonconforming finite element methods
Numerische Mathematik
Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
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In this work we derive and analyze a posteriori error estimators for low-order nonconforming finite element methods of the linear elasticity problem on both triangular and quadrilateral meshes, with hanging nodes allowed for local mesh refinement. First, it is shown that equilibrated Neumann data on interelement boundaries are simply given by the local weak residuals of the numerical solution. The first error estimator is then obtained by applying the equilibrated residual method with this set of Neumann data. From this implicit estimator we also derive two explicit error estimators, one of which is similar to the one proposed by Dorfler and Ainsworth (2005) [24] for the Stokes problem. It is established that all these error estimators are reliable and efficient in a robust way with respect to the Lame constants. The main advantage of our error estimators is that they yield guaranteed, i.e., constant-free upper bounds for the energy-like error (up to higher order terms due to data oscillation) when a good estimate for the inf-sup constant is available, which is confirmed by some numerical results.