A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface

Liang Wang; Xinpeng Yuan; Chunguang Xiong; Huibin Wu

doi:10.1016/j.cma.2021.114342

A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface

Liang Wang, Xinpeng Yuan, Chunguang Xiong^*, Huibin Wu

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we extend the discontinuous Galerkin (DG) isogeometric analysis (IgA) methods to solve nonlinear convection (Burgers) problems on implicitly defined surfaces or manifold. We establish an a priori error estimate for space semidiscretization with the sub-optimal convergence order in the L². We prove that the resulting methods can be implemented as efficiently as they are for the case of flat space or Euclidean space. The theoretical results are illustrated by two numerical experiments.

Original language	English
Article number	114342
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	390
DOIs	https://doi.org/10.1016/j.cma.2021.114342
Publication status	Published - 15 Feb 2022

Keywords

A priori error estimate
Burgers equation
Discontinuous Galerkin (DG)
Isogeometric analysis (IgA)
Manifold
Surface

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10.1016/j.cma.2021.114342

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title = "A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface",

abstract = "In this paper, we extend the discontinuous Galerkin (DG) isogeometric analysis (IgA) methods to solve nonlinear convection (Burgers) problems on implicitly defined surfaces or manifold. We establish an a priori error estimate for space semidiscretization with the sub-optimal convergence order in the L2. We prove that the resulting methods can be implemented as efficiently as they are for the case of flat space or Euclidean space. The theoretical results are illustrated by two numerical experiments.",

keywords = "A priori error estimate, Burgers equation, Discontinuous Galerkin (DG), Isogeometric analysis (IgA), Manifold, Surface",

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T1 - A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface

AU - Wang, Liang

AU - Yuan, Xinpeng

AU - Xiong, Chunguang

AU - Wu, Huibin

PY - 2022/2/15

Y1 - 2022/2/15

N2 - In this paper, we extend the discontinuous Galerkin (DG) isogeometric analysis (IgA) methods to solve nonlinear convection (Burgers) problems on implicitly defined surfaces or manifold. We establish an a priori error estimate for space semidiscretization with the sub-optimal convergence order in the L2. We prove that the resulting methods can be implemented as efficiently as they are for the case of flat space or Euclidean space. The theoretical results are illustrated by two numerical experiments.

AB - In this paper, we extend the discontinuous Galerkin (DG) isogeometric analysis (IgA) methods to solve nonlinear convection (Burgers) problems on implicitly defined surfaces or manifold. We establish an a priori error estimate for space semidiscretization with the sub-optimal convergence order in the L2. We prove that the resulting methods can be implemented as efficiently as they are for the case of flat space or Euclidean space. The theoretical results are illustrated by two numerical experiments.

KW - A priori error estimate

KW - Burgers equation

KW - Discontinuous Galerkin (DG)

KW - Isogeometric analysis (IgA)

KW - Manifold

KW - Surface

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DO - 10.1016/j.cma.2021.114342

M3 - Article

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SN - 0045-7825

VL - 390

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 114342

ER -

A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface

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Keywords

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