TY - JOUR
T1 - A priori error analysis for an isogeometric discontinuous Galerkin approximation for convection problems on surfaces
AU - Wang, Liang
AU - Yuan, Xinpeng
AU - Xiong, Chunguang
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2023/1/1
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.
KW - A priori error analysis
KW - Convection problems on surfaces
KW - Discontinuous Galerkin
KW - Isogeometric analysis
UR - http://www.scopus.com/inward/record.url?scp=85142450036&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2022.115638
DO - 10.1016/j.cma.2022.115638
M3 - Article
AN - SCOPUS:85142450036
SN - 0045-7825
VL - 403
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 115638
ER -