Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem

Abstract

This paper compares different a posteriori error estimators for nonconforming first-order Crouzeix–Raviart finite element methods for simple second-order partial differential equations. All suggested error estimators yield a guaranteed upper bound of the discrete energy error up to oscillation terms with explicit constants. Novel equilibration techniques and an improved interpolation operator for the design of conforming approximations of the discrete nonconforming finite element solution perform very well in an error estimator competition with six benchmark examples.