A residual based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a Virtual Element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based error estimator that does not involve any term related to the Virtual Element stabilization. Numerical results display a very good behaviour of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.

A Residual A Posteriori error estimate for the Virtual Element Method / Berrone, Stefano; Borio, Andrea. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 27:8(2017), pp. 1423-1458. [10.1142/S0218202517500233]

A Residual A Posteriori error estimate for the Virtual Element Method

BERRONE, Stefano;BORIO, ANDREA
2017

Abstract

A residual based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a Virtual Element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based error estimator that does not involve any term related to the Virtual Element stabilization. Numerical results display a very good behaviour of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2666363
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