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 scrC 1-conforming piecewise polynomial space and is instead based on an elliptic reconstruction of the discrete solution to the H2 space and a generalized Helmholtz decomposition of the error. This is the first hp-version error estimator for the biharmonic problem in two and three dimensions. The practical behavior of the estimator is investigated through numerical examples in two and three dimensions.

Dong, Z., Mascotto, L., Sutton, O. (2021). Residual-based a posteriori error estimates for hp -discontinuous galerkin discretizations of the biharmonic problem. SIAM JOURNAL ON NUMERICAL ANALYSIS, 59(3), 1273-1298 [10.1137/20M1364114].

Residual-based a posteriori error estimates for hp -discontinuous galerkin discretizations of the biharmonic problem

Mascotto, L
;
2021

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 scrC 1-conforming piecewise polynomial space and is instead based on an elliptic reconstruction of the discrete solution to the H2 space and a generalized Helmholtz decomposition of the error. This is the first hp-version error estimator for the biharmonic problem in two and three dimensions. The practical behavior of the estimator is investigated through numerical examples in two and three dimensions.
Articolo in rivista - Articolo scientifico
A posteriori error analysis; Adaptivity; Discontinuous Galerkin methods; Fourth order PDEs; Hp-Galerkin methods; Polynomial inverse estimates;
English
13-mag-2021
2021
59
3
1273
1298
none
Dong, Z., Mascotto, L., Sutton, O. (2021). Residual-based a posteriori error estimates for hp -discontinuous galerkin discretizations of the biharmonic problem. SIAM JOURNAL ON NUMERICAL ANALYSIS, 59(3), 1273-1298 [10.1137/20M1364114].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/329750
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