Computable a posteriori error bounds for a large class of nonconforming finite element methods are provided for a model Poisson-problem in two and three space dimensions. Besides a refined residual-based a posteriori error estimate, an averaging estimator is established and an L 2 -estimate is included. The a posteriori error estimates are reliable and efficient; the proof of reliability relies on a Helmholtz decomposition.
A computable error estimate is established for the model case of the Poisson‐problem. This enables an efficient method in applying the nonconforming Crouzeix‐Raviart Elements for adaptive refinement techniques. We study reliability and efficiency of the proposed algorithm both theoretically and numerically.
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