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

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 k + 21, 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.(c) 2022 Elsevier B.V. All rights reserved.