Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Numerical Analysis Year : 2021

Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem

Abstract

We introduce a residual-based a posteriori error estimator for a novel hp-version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimensions. We prove that the error estimate provides an upper bound and a local lower bound on the error and that the lower bound is robust to the local mesh size but not the local polynomial degree. The suboptimality in terms of the polynomial degree is fully explicit and grows at most algebraically. Our analysis does not require the existence of a C1-conforming piecewise polynomial space and is instead based on an elliptic reconstruction of the discrete solution to the H2 space and a generalised Helmholtz decomposition of the error. This is the first hp-version error estimator for the biharmonic problem in two and three dimensions. The practical behaviour of the estimator is investigated through numerical examples in two and three dimensions.
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Dates and versions

hal-03107210 , version 1 (12-01-2021)
hal-03107210 , version 2 (15-02-2021)

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Cite

Zhaonan Dong, Lorenzo Mascotto, Oliver J Sutton. Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem. SIAM Journal on Numerical Analysis, 2021, 59 (3), pp.1273--1298. ⟨10.1137/20M1364114⟩. ⟨hal-03107210v2⟩
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