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

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
文章编号	114342
期刊	Computer Methods in Applied Mechanics and Engineering
卷	390
DOI	https://doi.org/10.1016/j.cma.2021.114342
出版状态	已出版 - 15 2月 2022

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Wang, L., Yuan, X., Xiong, C., & Wu, H. (2022). A priori error analysis of discontinuous Galerkin isogeometric analysis approximations of Burgers on surface. Computer Methods in Applied Mechanics and Engineering, 390, 文章 114342. https://doi.org/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",

author = "Liang Wang and Xinpeng Yuan and Chunguang Xiong and Huibin Wu",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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doi = "10.1016/j.cma.2021.114342",

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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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U2 - 10.1016/j.cma.2021.114342

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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