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Cockburn, B., Hou, S. and Shu, C.-W. (1990) The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws IV: The Multidimensional Case. Mathematics of Computation, 54, 545-581.

has been cited by the following article:

• TITLE: An Isogeometric Error Estimate for Transport Equation in 2D

  AUTHORS: Aurélien Goudjo, Uriel Aguemon

  KEYWORDS: Error Estimate, Isogeometric Method, The Two Stage Heun Scheme, Transport Equation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.9 No.9, September 18, 2019

  ABSTRACT: In this paper, an isogeometric error estimate for transport equation is obtained in 2D to prove the convergence of isogeometric method. The result that we have obtained, generalizes Ern result, got in finite elements method. For the time discretization, the two stage Heun scheme is used to prove this result. For a polynomial of degree k≥1, the order of convergence in space is 2 and in time is .