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

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.