A posteriori error estimates of hp-discontinuous Galerkin method for strongly nonlinear elliptic problems

Chunjia Bi; Cheng Wang; Yanping Lin

doi:10.1016/j.cma.2015.08.017

A posteriori error estimates of hp-discontinuous Galerkin method for strongly nonlinear elliptic problems

Chunjia Bi, Cheng Wang, Yanping Lin

Research output: Journal article publication › Journal article › Academic research › peer-review

6 Citations (Scopus)

Abstract

In this paper, we study the residual-based a posteriori error estimates of hp-discontinuous Galerkin finite element methods for strongly nonlinear elliptic boundary value problems. Computable upper and lower bounds on the error are derived in a natural mesh-dependent energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. Numerical experiments are also provided to illustrate the performance of the proposed estimators.

Original language	English
Pages (from-to)	140-166
Number of pages	27
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	297
DOIs	https://doi.org/10.1016/j.cma.2015.08.017
Publication status	Published - 1 Jan 2015

Keywords

A posteriori error estimates
hp-discontinuous Galerkin method
Residual estimator
Strongly nonlinear elliptic problems

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2015.08.017

Cite this

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abstract = "In this paper, we study the residual-based a posteriori error estimates of hp-discontinuous Galerkin finite element methods for strongly nonlinear elliptic boundary value problems. Computable upper and lower bounds on the error are derived in a natural mesh-dependent energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. Numerical experiments are also provided to illustrate the performance of the proposed estimators.",

keywords = "A posteriori error estimates, hp-discontinuous Galerkin method, Residual estimator, Strongly nonlinear elliptic problems",

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AB - In this paper, we study the residual-based a posteriori error estimates of hp-discontinuous Galerkin finite element methods for strongly nonlinear elliptic boundary value problems. Computable upper and lower bounds on the error are derived in a natural mesh-dependent energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. Numerical experiments are also provided to illustrate the performance of the proposed estimators.

KW - A posteriori error estimates

KW - hp-discontinuous Galerkin method

KW - Residual estimator

KW - Strongly nonlinear elliptic problems

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DO - 10.1016/j.cma.2015.08.017

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EP - 166

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

A posteriori error estimates of hp-discontinuous Galerkin method for strongly nonlinear elliptic problems

Abstract

Keywords

ASJC Scopus subject areas

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