A priori error analysis for an isogeometric discontinuous Galerkin approximation for convection problems on surfaces

Liang Wang; Xinpeng Yuan; Chunguang Xiong

doi:10.1016/j.cma.2022.115638

A priori error analysis for an isogeometric discontinuous Galerkin approximation for convection problems on surfaces

Liang Wang, Xinpeng Yuan, Chunguang Xiong^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

1 Citation (Scopus)

Abstract

In this paper, we identify and study the new isogeometric analysis penalty discontinuous Galerkin (DG) methods of convection problems on implicitly defined surfaces with optimal convergence properties. Like all other known discontinuous Galerkin methods on flat space or Euclidean space using polynomials of degree k≥0 for the unknown, the orders of convergence in L² norm and DG norm are k+1 and [Formula presented], respectively, which shows the resulting methods on surfaces 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	115638
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	403
DOIs	https://doi.org/10.1016/j.cma.2022.115638
Publication status	Published - 1 Jan 2023

Keywords

A priori error analysis
Convection problems on surfaces
Discontinuous Galerkin
Isogeometric analysis

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10.1016/j.cma.2022.115638

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Wang, L., Yuan, X., & Xiong, C. (2023). A priori error analysis for an isogeometric discontinuous Galerkin approximation for convection problems on surfaces. Computer Methods in Applied Mechanics and Engineering, 403, Article 115638. https://doi.org/10.1016/j.cma.2022.115638

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abstract = "In this paper, we identify and study the new isogeometric analysis penalty discontinuous Galerkin (DG) methods of convection problems on implicitly defined surfaces with optimal convergence properties. Like all other known discontinuous Galerkin methods on flat space or Euclidean space using polynomials of degree k≥0 for the unknown, the orders of convergence in L2 norm and DG norm are k+1 and [Formula presented], respectively, which shows the resulting methods on surfaces 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.",

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AU - Wang, Liang

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AU - Xiong, Chunguang

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Y1 - 2023/1/1

N2 - In this paper, we identify and study the new isogeometric analysis penalty discontinuous Galerkin (DG) methods of convection problems on implicitly defined surfaces with optimal convergence properties. Like all other known discontinuous Galerkin methods on flat space or Euclidean space using polynomials of degree k≥0 for the unknown, the orders of convergence in L2 norm and DG norm are k+1 and [Formula presented], respectively, which shows the resulting methods on surfaces 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 identify and study the new isogeometric analysis penalty discontinuous Galerkin (DG) methods of convection problems on implicitly defined surfaces with optimal convergence properties. Like all other known discontinuous Galerkin methods on flat space or Euclidean space using polynomials of degree k≥0 for the unknown, the orders of convergence in L2 norm and DG norm are k+1 and [Formula presented], respectively, which shows the resulting methods on surfaces 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.

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A priori error analysis for an isogeometric discontinuous Galerkin approximation for convection problems on surfaces

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